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HARVARD    UNIVERSITY. 


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MUSEUM  OF  COMPARATIVE  ZOOLOGY. 


COMPARATIVE  ZOOLOGY. 


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TRANSACTIONS 


CONNECTICUT  ACADEMY 


ARTS   AND   SCIENCES. 


VOI.XJ]ME     III 


NEW    HAVEN: 
PUBLISHED    BY    THE    ACADEMY. 

"^1874  to  1878. 

Tutlle,  Morehouse  A  Taylor,  Printers,  New  Haven. 


CONTEISTTS 


PAGE 


List  of  Additjons  to  the  Library,....    ..    ...    ....       y 

Art.  I. — Report  on  the  dredgixgs  in  the  regiox  of  St. 

George's    Banks,   ix    1872.     By   S.   1.   Smith  and  O. 

Harger.     Plates  1  -8, 1 

Art.  IL — Descriptions  of  new  and  rare  species  of  Hy- 

DROIDS     FROM     THE     NeW     EnGLAND     COAST.         By    S.     F. 

Clark.     Plates  9-10,  _ 58 

Ar'J'.  III. — On  the  Chondrodite  from  the  Tilly-Foster 
IRON  MINE,  Brewster,  N.  Y.  By  E.  S.  Dana.  Plates 
11-13, 67 

Art.  IV. — On  the  Transcendental  curves  sin  y  sin  iny=. 
a  %\n  X  ^\w  nx-\-h.  By  H.  A.  Xewton  and  A.  W. 
Philips.     Plates  14-37, . 97 

Art.  V. — On  the  equilibrium  of  heterogeneous  sub- 
stances.    By  J.  W.  GiBBS.     First  Part, 108 

Art.  VI. — The  Hydroids  of  the  Pacific  coast  of  the 
United  States  south  of  Vancouver  Island,  with  a 

REPORT    upon  those  IN  THE  MuSEUM  OF  YalE  ColLEGE. 

By  S.  F.  Clark.     Plates  38-41, 249 

Art.  VII. — On  the  anatomy  and  habits  of  Nereis  virens. 

By  F.  M.  Tubnbull.     Plates  42-44, 265 

Art.  VIII. — Median  and  paired  fins,  a  contribution  to 

THE  history  of  VERTEBRATE  LIMBS.      By  J.   K.  ThACHER. 

Plates  49-60, 281 

Art.  IX. — Early  stages  of  Hippa  talpoida,  with  a  note 

ON    the    structure  of  the  MANDIBLES    AND    MAXILLA    IN 

HipPA  AND  Remipes.     By  S.  I.  Smith.     Plates  45-48,  311 
Art.   X.  —  On   the    equilibrium  of  heterogeneous   sub- 
stances (concluded).     By  J.  W.  Gibbs, 343 


OFFICERS  OF  THE  ACADEMY. 


President, 
ELIAS   LOOMIS. 

Vice-President, 
HUBERT  A.   NEWTON. 

Secretary, 
OSCAR   HARGER. 

Librarian, 
ADDISON  VAN    NAME. 

Treasurer, 
HENRY   C.    KINGSLEY. 

Publishing  Cormn ittee, 
HUBERT   A.   NEWTON,  ELIAS   LOOMIS, 

GEORGE   J.   BRUSH,  ADDISON   E.  VERRILL, 

CHESTER   S.  LYMAN,  WILLIAM  D.  WHITNEY. 

Auditing  Committee, 

HUBERT   A.  NEWTON,         DANIEL   C.  EATON, 

HENRY  T.    BLAKE. 


ADDITIOlSrS  TO   THE   LIBRAEY 

From  December  1,  1873,  to  June  1,  1876. 


Anierican  Association  for  the  Advancement  of  Science.     Proceedings.    Twenty-second. 

twenty -third  Meetings.    8".     Memoirs.  I.   4  .     Salem,  1874-5. 
Alr.\ny. — Institute.     Transactions.  Vol.  VIT,  VIII.     1872-6.   8°.     Proceedings.    Vol. 
I.  a-4,  II.  1.     1871-4.  .8°. 

New    York    State    Cabinet   of  Natural   History.     Twenty-third,    twenty-fifth 

Annual  Reports.     1870-2.  8°. 

New  York  State  Library.     Fifty-sixth  Annual  Report.     1874.    8°. 

Boston. — American   Academy  of   Arts  and   Sciences.     Proceedings.     Vol.   VIII-X. 
1868-75.    8°. 

Society   of   Natural  History.     Memou's.     Vol.  II.  i.  1,  ii.  4,  iii.  1-5,  iv.  1-4. 

1871-6.   4°.    Proceedings.    Vol.  XV.  4,  XVI,  XVII,  XVIII.  1-2.    1873-6. 
8  .     Henz,  N.  M.     The  Spiders  of  the  United  States.     (Occasional  Papers. 
II).      1875.    8". 
Buffalo. — Society  of  Natural  Sciences.     Bulletin.   Vol.  I.  4,  II.  III.  1-2.     1874-6.    8°. 
CAMBRIDGE. — Museum  of  Com'parative  Zoology.     Illustrated  Catalogue.     No.  IV-VIII. 
1871-4.    4°.     Bulletin.     Vol.  II.  3-5,  III.  1-14.     1871-6.    8".     Annual 
Report.     1870-1875.    8°. 
'him'HEXPOijis.-- Minnesota  Academy  of  Natural  Sciences.     Bulletin.     1874.    8°. 
New  York. — Lyceum  of  Natural  History.     Annals.    Vol.  XI.  3-6.     1875.    8°. 
PouGHKEEPSiE. — Society  of  Natural  Science.     Proceedings.    Vol.  I.  1-2.     1876.    8°. 
St.  Louis. — Academy  of  Science.     Transactions.     Vol.  III.  2.     1875.    8°. 
Sxh^M.— Essex  Institute.     Bulletin.     Vol.  V.  6-12,  VI,  VII.  1-7.     1873-5.    8°. 

Peabody  Academy  of  Science.     Memoirs.     Vol.  I.  4.     1875.   4\ 

San  Francisco. —  California  Academy  of   Sciences.      Proceedings.     Vol.   I.    1854-7 

(2d  ed.  187.3),  III.  2.     1873.    8°. 
Savannah. —  Georgia  Historical   Society.      Jones,  C.  C,  Jr.      Se.'-geant  Wm.  Jasper. 

An  Address  before  the  Georgia  Historical  Society,  Jan.  3,  1876.    8°. 
Washington. — Surgeon   GeneraVs   Office.      Annual  Report  of   tlie  Surgeon  General, 
U.  S.  Army.     1874.     8°.     Circular  No.  8.     Report  on  the  Hygiene  of 
the  U.  S.  Army.     1875.    4\ 
United  States  Naval  Observatory.     Astronomical  and  Meteorological  Observa- 
tions.    1871,  1873.    4". 
Worcester. — A77ierican  Antiquarian  Society.     Proceedings.    No.  62-65.    1874-5.    8°. 


vi  Additions  to  the  Lihrary. 

Amsterdam. — Koninklijke  Akademie  van  Wetensrhappen.     Yerslagen  en  Mededeelingen. 
Afdeel.  Natuurkunde.  Tweede  Reeks.  Deel  VII.  ISTS.    8".     Jaarboek. 
1872.    8°. 
Augsburg. — Naturhistorischer  Verein.     Bericht  XXII,  XXIII.     1873-5.    8°. 
Basel. — Naturforschende  Geselbchaft.    Bericht  iiber  die  Verhandlungen.  I-YIII.    1 835- 

1849.    8°.     Yerhandhmgen.     Theil  YI.  1-2.     1874-5.    8°. 
B ATA VI A. — Natuurkundige  Vereeniging.     Natimrkundig  Tijdschrift  voor  Nederlandsch 
Indie.     Deel  XXII,  XXIII.     1871-3.    s°. 

Societe  des  Arts  et  des  Sciences.     Tijdschrift.  Yol.  XX.  4-fi,  XXI.  1-2.     1872-4. 

8°.    Notulen.  X.  4.  XI.  1-4.     1873-4.    8°.     Codicum  Arabicoriim  ( 'atalogus. 
1873.    8°.     Alphabetische  Lijst  van  Kaarten.     1873.    8°. 
Belfast. — Natural  History  and  Philosophical  Society.     Proceedings.  Session  1872-3, 

1873-4,  1874-5.    8°. 

Berlin. — Konigliche  Akademie  der    Wissenschaften.       Physikalische   Abhandlungen. 

1838,  1841,  1842.  1845,   1849.    4°.      Mathematische  Abhandlungen.     1845. 

4°.      Bericht    iiber    die     Yerhandhmgen.       1854-5.     8°.       Monatsbericht. 

1856-9.     8°. 

Bologna. — Accademia  delle  Scienze  delV  Instituto  di  Bologna.     Rendiconto.     1873-4.  8". 

Bonn. — Naturhistorischer  Verein  der  preussischen  Rheinlande  und  Westplialens.     Yer- 

handlungen.     Jahrg.  XXIX.  2,  XXX,  XXXI,  XXXII.  1.     1872-5.    8°. 
Bordeaux. — Societe  des   Sciences  Physiques  et  Naturelles.      Memoires.       T.  IX,   X, 
II.  Ser.  I.  1.     1873-5.    8°. 

Societe  Linneenne.     Actes.     T.  XXYII.  2,  XXYIII.     1872.    8°. 

Bremen. — Naturwissenschaftlicher  Verein.     Abhandlungen.  Bd.  III.  4,  IV.  1.      1873-4, 

8°.  Beilage.  No.  3.  1873.  4°. 
Brunn. — Naturforscher  Verein.  Yerhandhmgen.  Bd.  Y,  VI,  XI,  XII.  1866-74.  8°. 
Brussels. — Academie  Royale  des  Sciences,  des  Lettres  et  des  Beaux-Arts  de  Belgique, 
Memoires.  T.  XL.  1873.  4°.  Memoires  Couronnes  et  Memoires  des 
Savants  I^trangers.  T.  XXXYII,  XXXVIII.  1873-4.  4°.  Memoires 
Couronnes  et  Autres  Memoires.  T.  XXIII.  1873.  8°.  Bulletins. 
II.  Ser.  T.  XXXY-XXXYII.  1872-4.  8°.  Annuaire.  1874.  8°. 
Centieme  anniversaire  de  fondation.     1872.     2  vols.    8°. 

Observatoire  Royal.     Annales.     T.  XXI,  XXII.     1872-3.    4°. 

Observations  des  phenomenes  periodiques.  1872.  4°.  Notices  extraits 
de  r  Annuaire  pour  1874.  16°.  Quetelet,  A.  Congres  international 
de  statistique.  1873.  4°.  Quetelet,  E.  La  comete  de  Coggia.  8°. 
pp.  10.      Quetelet,  E.    Rapport  sur  I'areography  de  M.  Terby.    8  \    p.  6. 

Societe  Entomologique  de  Belgique.    Annales.      T.  I-XIV,  XYI.     1857-1873. 

8°.     Compte-rendu.     Ser.  IL     No.  18.     1875.    8°. 

Societe  Geologique  de  Belgique.     Annales.     T.  I.     1874.    8°. 

Buenos    Ayres. — Academia   Nacional  de    Ciencins  Exactas.      Boletin.     Entrega  I. 

1874.    8°. 
Calcutta.— A9ia<ic  Society  of  Bengal.    Journal.  1873.  I.  2-4,  II.  3-4;   1874;  1875, 1., 

II.  1-3.    8°.     Proceedings.     1873.  v-x,  1874,  1875.     8°. 
Carlsruhe. — Polytechnische  Schule.     Programm.     1875-6.    8°.     Riffel,  A.  Ueber  die 
anatomischen  und  physiologischen    Eigenschaften  der  ausseren  Haut. 
Tubingen,  1875.    8°. 


Additiuns  to  the  Lihrary.  vii 

Catania. — Accademia    Gioenia  di  Scienze  Naturali.     Atti.      Ser.  III.     T.  VII,  VIII. 

1872-3.   4°.   Carta  geologica  della  citta  di  Catania  e  dintonii.    Per  Car- 

melo  Scinto-Patti.    8  Tavole. 
Chemnitz. — Naturwibsenschaftlidie  Gesellschaft.     Bericht  IV.     1873.    8°. 
Cherbourg. — Societe  Nationale  des  Sciences  Naturelks.     Memoires.     T.  XVII,  XVIII. 

1873.  8".    Catalogue  de  la  bibliotheque.     2"*  partie,  1"  livr.     1873.    8°. 
Chur. — Naturfurschende   Gesellschaft  Graubiindens.     Jahresbericht.    Neue  Folge.     XV 

-XVII.     18G9-72.    8°. 
Copenhagen.  —  Kongelige  Danske  Videnskaberaes  Selskab.     Oversigt  over  Forliandlin- 

ger.     1873,  1874,  1875,  i.    8°. 
Danzig. — Naturforschende  Gesellschaft     SchrLfteu.     Neue  Folge.  Bd.  III.  2-3.     1873-4. 

8°. 
Dijon. — Academie  des  Sciences,   Arts  et  Belles  Lettres.      Memoires.      III.  Ser.     T.  I. 

1871-3.    8°. 
DORPAT. —  Gelehfte   Estnische    Gesellscliaft.      Verhaudluiigeu.    Bd.  VIII.  2.     1875.    8°. 

Sitzungstaericht.     1874.   8°. 
Naturforscher  Gesellschaft.     Sitzung.sberichte.  Bd.  III.  1-6,  IV.  1.     1869-75. 

8°.     Archiv  fiir  die  Naturkunde  Liv-,  Ehsl-  uud  Kurland.s.     I.  Ser.  Bd. 

V.  1-4,  VI,  VII,  1-4.     1870-5.    II.  Ser.  Bd.  V,  VII.  1-2.    1867-75.    8  . 
Dresden. — Kais.  Leopold.-  Carolin.  Deutsche  Akademie  der  Naturforscher.     Leopoldiiia. 

HeftVII-X.     1871-4.    4°. 
Naturwissenschaftliche  Gesellschaft  Isis.     Sitzungsberichte.    1873,  Apr. -Dec, 

1874,  Jan.-Sept.,  1875,  Jau.-Dec.   8°. 

Verein  fur  Erdkunde.     Jahresbericht.     X,  XI,  XII.     1874-5.    8°. 

Dublin. — Royal  Irish  Academy.     Transaetious.    Vol.  XXIV;  Antiquities,  Ft.  ix;  Vol. 

XXV;  Science,  Pt.  i-xx.  1872-5.   4^.     Proceedings.    Vol.  X.  4;  Series 

II.  Vol.  II.  1-3.     1870-5.    8°. 
Edinburgh. — Geological  Society.     Transactions.     Vol.  II.  3.     1874.    8°. 
Emden. — Naktrfwschende  Gesellschaft.     Kleine  Schriiten.  XVII.     Hannover,  1875.   4°. 

Jahresbericht.  LIX,  LX.     1873-4.    8°. 
Erfurt. — Konigl.  Akademie  gemeinniitziger   Wissenschaften.      Jalirbuch.     Neue  Folge. 

Heft.  VII.     1873.    8°. 
Falmouth.  —  Royal    Cornwall  Polytechnic    Society.      Forty-second   Annual   Report. 

1874.     8°. 
FiRENZE. — R.  Comitato  Geohgico  d'ltalia.     Bolletino.  1873,  1874,  1875.  i-iv.   8°. 
Frankfurt  a.  M. — Neue  Zoologische  Gesellschaft.     Der   Zoologische  Garten.      Jahrg. 

XIV.  7-12,  XV,  XVI.   1-6.     1873-5.    8°. 
Freiburg  i.  B. — NatMrforschende  Gesellschaft.     Berichte.  Bd.  VI.  1-2.     1873.   8'. 
Geneve. — Institut  National  Genevois.     Bulletin.     T.  XX.     1875.   8". 
Societe  de  Physique  et  d^  Histoire  Naturelle.      Memoires.      T.  XXIII.  XXIV. 

1.  1873-5.    4°. 
Glasgow. — Philosophical  Society.     Proceedings.     Vol.  IX.     1873-5.    8°. 
Gorlitz. — Naturforschende  Gesellschaft.     Abhandhmgen.     Bd.  XV.     1875.    8°. 
Goteborg.  —  Kongl.  Vetenskaps  och  Vitterhets-Samhallr'.       Handlingar.    Ny  Tidsfoljd. 

Haftet  XII-XIV.     1873-4.    8°. 
Halle. — Naturfarschende   Gesellschaft.      Abhandhmgen.      Bd.    XII.  3-4,  XIII.  2.   4°. 

Bericht.  1873,  1874.    4". 
Nalurwissenschaftlicher   Verein  fiir  Sachsen  und   Thilringen.     Zeitschrift  der 

gesammten  Naturwissenschaften.     Bd.  VII-X.     Berlin,  1873-4.    8°. 


viii  Additions  lo  the  Lihrary. 

Hamburg. — Xaturwissemchafllicher  Verein.    Abhandlungon.  Bd.  V. -i,  VI.  1.    1873.  4". 
Hannover. — Naturhislorische  Gesellschaft.     Jahresbericht.  XXII-XXIV.    1872-4.    8°. 
Harlem. — Musee  Teyler.     Archives.     Vol.  III.  3.     1873.  8°. 
Heidelberg.  —  NaturMstorisch-Medecinischer   Verein.     Verhandlungen.     Neue  Folge. 

Bd.  I.  1,  3.     1874-6.    8°. 
Helsingfors. — Societas  Sdentiarum  Fennica.       Ofversigt   af  Forhandlingar.      XIV- 

XVI.    1871-4.    8'.   Bidrag  till  Kannedom  af  Finlands  Natur  och  Folk. 

Haft.  XVIII,  XIX,  XXI,  XXII,  XXIII.     1871-3.    8\ 
Hermannstadt. — Siehenhurgischer  Verein.     Verhandlungen.     Jahrg.  XXV.  1875.    8". 
Hobart  Town. — Royal  Society  of  Tasmania.     Monthly  Notices  for  1872.    8". 
KoNiGSBERG. — Konigl.  physikalisch-  okonomische  Gesellschaft.    Schriften.     Jahrg.  XIV- 

XV.     1873-4.    4°. 
Krakau. — K.k.  Ste7-nivarte.    Materialy  do  Kllimatografii  Galicyi.     Rok  1872-1874.     8'. 
Lausanne. — Societe   Vaudoise  des  Sciences  Naturelles.     Bulletin.     II.  Ser.     No.  64-65, 

71-75.     1870-1876.    8°. 
Leiden. — Sternwarte.     Annalen.     Bd.  IV.     Haag,  1875.   4^ 
Leipzig. — Astronomische  Gesellschaft.      Vierteljahrsschrift.     Jahrg.  VIII.  3-4,  IX,  X. 

1-3.  1873-5.    8°.     Publication  XIII.     1874.    4". 
Liege. — Societe  Royalf.  des  Sciences.     Memoires.     II.  Ser.     T.  IV,  V.     1873-4.    8". 
LiNZ. — Handels- und  Geiuerbekammer.    Bericht.  1870,  1871,  1872.   8°.    Bericht  iiber  die 

Lage  und  Bediirfnisse  des  Kleingewerbes  in  Oberosterreich.     1872.    8  . 
Liverpool. — Literary  and  Philosophical  Society.      Proceedings.     No.  XXVII-XXIX. 

1872-5.    8°. 
London. — Mathematical  Society.     Proceedings.     No.  62-86.     1873-6.     8°. 
Luxembourg. — Institut  Royal  Grand-Ducal.     Publications.     T.  XIII.     Section  des  Sci. 

Nat.  et  Mathemat.      T.  XIV,  XV.      1873-5.    8°.      Observations  Meteo- 

rologiques  faites  a  Luxembourg  par  F.  Renter.     Vol.  II.     1874.    8  . 
Lyon. — Academie  des  Sciences,  Belles-Lettres  et  Arts.     Memoires.    Classe  des  Sciences. 

T.  XX.     1873-4.    8=. 
Manchester. — Literary  and  Philosophical  Society.      Memoirs.      III.    Ser.  Vol.  IV. 

1871.   8°.     Proceedings.     A^ol.  VIII-XII.     1869-73.  8°. 

Scientific  Students  Association.     Annual  Report.     1872,1873.    8". 

Melbourne. — Royal  Society  of  Victoria.     Transactions  and  Proceedings.     Vol.  X,  XI. 

1874.  8°. 

Metz. — Academie.       Memoires.      Annee  L-LV.      1868-74.    8°.       Tables  generales. 

1819-1871.    8\ 
Mexico. — Sociedad  de   Geografia  y  Estadistica.      Boletin.      Ill  Epocha.      T.  II.  5-6. 

1875.  8°. 

MiLANO. — Reale  Instituio  Lomhardo.  Rendiconti.  Serie  II.  Vol.  VI.  6-20.  VII.  1-16. 
1873-4.    8  . 

Reale   Osservatorio  di  Brera.      Publicazione.      No.   II,  IV,  V,  VII-X. 

1873-5.    4°. 

Societd  Italiana  di  Scienze  Xaturali.     Atti.     Vol.  XV.  3-5.  XVI,  XVII.  1-3. 

1872-5.    8°.  . 

MONTPELLiER. — Academie  des  Sciences  et  des  Lettres,  Memoires.  Lettres,  T.  V.  4 ;  Sci- 
ences, T.  VIIL  2;  Medecine,  T.  IV.  6.     1870-2.    4°. 

Moscow, — Societe  Imperiale  des Naturalistes.  Nouveaux  Memoires,  T-  XIII.  4,  1874, 
4°.    Bulletin.     1873,  ii-iv,  1874,  i-iv.   8°, 


Additions  to  the  Library. 


IX 


MUNCHEN. — Konkjl.  Bayerische  Akademie  der  Wissenschaften.    8itziingsberifhte  der  phi- 

losoph.-  philolog.  und  histor.  Classe.      1872.  iv-v,  1873,  1874.  i-iii.    8  . 

Sitzungsberichte  der  mathemat.-physikal.  Classe.  1872.  iii,    1873.  1874. 

i-ii.     8". 

Bietz,  W.    Der    Antheil  der  konigl.  Bayer.  Akademie  an  der  Eutwick- 
lung  der  Electricitatslehre.     Miinchen,  1873.    4". 

Bisc'hoff,  T.  L.  W.  von.     Ueber  den  Einfluss  des  Freih.  Justus  v.  Liebig 
auf  die  Entwicklung  der  Physiologie.     Miinchen,  1874.    4°. 

DoUinger,  J.  von.     Rede,  25  Juli,  1873.     Miinchen,  1874.    8". 

Pettenkofer,  Max  von.     Dr.  Justus  Freih.  von  Liebig.  zum  Gedaclitniss. 
Miinchen,  1874.    4°. 

Prantl,  K.  von.    Gedachtnissrede  auf  F.  A.  Trendelenburg.      Miinchen, 
1873.   4°. 

Vogel,  A.      Justus  Freili.  von  Liebig  als  Begriinder  der   Agrikultur- 
Chemie.     Miinchen,  1874.   4. 
Sternwarte.       Annalen.     Bd.   XIX.     1873.    8°.     Supplementbd.  XIII. 

1874.    8°. 
Landesioirtlischaftlicher  Verein  in  Boyern.     Haus-  nnd  Landwirthschafts 

Kalender.     1874.    4°. 
Napoli. — Societd  Reale  di  NapoU.      Accademia  delle  Scienze  Fisiclie  e  Matematiche. 

Atti.     Vol.  V.  1873.    4°     Rendiconto.     Anno  IX-XI.     1870-72.   4°. 
Neu-Brandenburg. —  Verein  dm-  Freunde  der  Naturgeschichte  in  Meckknbvjy.     Archiv. 

Jahrg.  XXVII-XXIX.     1873-5.     8°. 
Neuchatel. — Societe  des  Sciences  NatMrelles.     Bulletin.     T.  IX,  X.  1-2.     1871-5.    8". 
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Jahresversammlung  LVI.   8°. 
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Meteorologiska  Jagttagelser.     Bd.  XII-XIV.     1870-2.   4°. 

Minnesteckning  ofver  J.  A.  von  Hartniansdorff.     1872.    8°. 

Minnesteckning  ofver  Hans  Jarta.     1874.    8°. 
Stuttgart. —  Verein  fiir  vaterliindische   Naturkunde    in    Wilrttemberg.      Jahreshefte. 

Jahrg.  XXX,  XXXI.     1874-5    8°. 
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1873.    8°. 
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XXVIII.     1871-~1.    8°. 


Addiiiovs  in  the  Lihrcvn/.  xi 

WuRZBURG. —  Physihiliscli- rnedicinifiche  Gesellscha/f.     Sitzimgsberichte.    1868-74.    8"^. 

Festschrift  ziir  Feier  des  fiinfundzwanzigjahriges  Bestehens  der  Gresell- 

schaft.     1875.   4°. 

Kolliker.  A.     Festrede,  8.  December,  1874.    8°. 
Zurich. — Natwforschende  Gesellschaft.     Yierteljahrsshrift.     Jahrg.  XIV-XVII.     1869 

-72.    8°. 


Agardh,  J.  U.    Till  Algernes  Systematik.  Xya  Bidrag.    Lund,  1872.    4". 

Frmn  the  Author. 
Galle,  J.  G.     Ueber  eine  Bestimung  der  Sonnen-  ParaUaxe  aus  correspondirenden  Be- 
obachtungen  des  Planeten  Flora,  187.'?.     Breslau,  1875.    8'. 

From' the  Author. 
Haughton,  R.     Principles  of  Animal  Mechanics.     Second  Edition.     Lond.,  1873.    8". 

From  the  Author. 
Macodo,  J.  M.  de.     Notions  de  chorographie  du  Brezil.     Leipzig,  l87o.    8^. 
Schiner,  J.  R.     Diptera  Austrica.  I.     Wien,  1854. 

iSeparatabdruck  naturwiss.  Abhandlungen  aus  den  Schriften  des  zoolog.-botanischen 
Vereins,  in  Wien.     Wien,  1856.    8. 

From  Dr.  V.  Ploson. 
Meunier,  S.     Cours  de  geologic  compareo.     Paris,  1874.    8  . 

From  the' Author. 
Morren,  fi.     L'horticulture  a  rF,xposition  Universelle  de  Paris  de  1867.     Bruxelles, 
1870.    8\ 

Rapport  seculaire  sur  les  travaux  de  botanique  et  de  physiologic  vege- 

tale.     Bruxelles.    8^. 

Eloge  de  Jean- Theodore  Lacordaire.     Liege.  1870.    8". 

From  the  Author. 
Newberry,  J.  S.     The  Surface  Geology  of  Ohio.     (Jolumbos,  1874.    8^. 

Tlie    Structure   and    Relations   of   the  Dinicthys.       Witli    two   charts. 

Columbus,  1875.    8~. 

From  the  Author. 
Saussure,  H.  de.    Memoires  pour  servir  a  I'histoire  naturelle  de  Mexique,  des  Antilles 
et  des  Etats  Unis.     Premiere  livraison.     Crustacees.   Geneve,  1858.    8" 

From  the  Author. 
Winchell,  N.  H.    Geological  and  Natural  History  Survey  of  Minnesota.     Second  and 
third  Annual  Reports.  1873.  1874.     St.  Paul,  1874-5.    8°. 

From  the  Author. 


I.     Report  ox  the  Dr edgings  in  the  region  of  St.   George's 
Banks,  in   1872.*     By  S.  I.  Smith  and  O.  Harger. 


[Published  by  permission  of  tlie  Superintendent  of  the  U.  S.  Coast  Survey.] 


During  the  summer  of  1872,  a  series  of  dredgings  was  carried  on 
by  the  authors  in  the  neighhorliood  of  St.  George's  Banks.  The  work 
was  undertaken  at  the  instance  of  Professor  Baird,  United  States 
Commissioner  of  Fish  and  Fisheries,  and  carried  on,  through  the 
cooperation  of  the  Coast  Survey,  from  the  steamer  Bache,  on  board 
of  which  accommodations  were  furnished  for  two  persons,  with  the 
necessary  apparatus.  On  board  the  steamer  we  were  received  and 
treated  throughout  with  the  utmost  courtesy  by  Commander  J.  A. 
Howell,  and  the  other  officers  of  the  vessel.  Lieutenants  Jaques, 
Hagerman,  Jacob  and  Rush  ;  and  although  the  dredging  was  carried 
on  in  connection  with  the  special  hydrographic  work  of  the  Coast 
Survey,  all  these  gentlemen  manifested  a  degree  of  interest  in  our 
work  equal  to  that  which  they  felt  in  their  own. 

On  account  of  the  lateness  of  the  season  at  which  operations  were 
begun,  the  weather  was  most  of  the  time  cpiite  unfavorable  for  dredg- 
ing, so  that  the  number  of  hauls  made  with  the  dredge  was  much 
smaller  than  had  been  expected,  and  no  opportunities  were  afforded 
for  using  the  large  traAvl  or  the  rake  dredges  which  had  been  pro- 
vided, with  the  rest  of  the  outfit  for  the  natural  history  department 
of  the  expedition,  by  the  United  States  Fish  Commissioner.  Still,  the 
collections  which  were  made  from  these  comparatively  few  dredgings 
have  proved  rich  and  very  important,  giving  nearly  the  only  informa- 
tion which  we  possess  of  the  character  of  the  fauna  of  the  fishing 
banks,  and  adding  very  largely  to  the  knowledge  of  the  distribution, 
both  geographical  and  bathymetrical,  of  the  marine  animals  of  our 
northern  coast. 

*  The  text  of  this  report  was  written  and  presented  to  the  Superintendent  of  the 
Coast  Survey,  very  nearly  in  its  present  form,  in  December,  1872,  but  its  publication 
has  been  unavoidably  delayed  until  the  present.  The  figures  illustrating  some  of  the 
species  mentioned  have  been  added  since  the  report  was  first  prepared. 

Trans.  Connecticut  Acad.,  Vol,  III.  1  xily,  1874. 


2  Smith  and  Harger — St.  George's  Banks  Dredgings. 

After  we  were  obliged,  late  in  September,  to  leave  the  expedition. 
Prof.  A.  S,  Packard,  Jr.,  and  Mr.  Caleb  Cooke,  of  Salem,  Mass.,  went 
in  the  steamer  on  another  trip,  which  was  mainly  devoted  to  dredg- 
ing. On  this  trip  a  number  of  successful  hauls  were  made  at  differ- 
ent localities  along  the  northern  extremity  of  George's  Bank,  in  40  to 
150  fathoms.  The  region  visited  on  this  trip  was  quite  distant  from 
any  of  the  localities  examined  by  us,  and  the  bottom,  in  the  deeper 
dredgings,  was  of  an  entirely  different  character,  so  that  the  collec- 
tions made  by  Prof  Packard  and  Mr.  Cooke  contain  many  species 
not  found  by  us,  and  add  very  greatly  to  the  value  of  the  results. 

We  wish  specially  to  acknowledge  the  assistance  rendered  us  in 
the  preparation  of  this  report  by  Professor  Verrill,  who  has  identified 
all  the  worms  mentioned,  and  the  more  difficult  mollusks  and 
radiates. 

The  following  table  will  facilitate  references  to  the  localities  at 
which  the  dredgings  were  made.  The  letters  in  the  first  column  are 
the  same  as  those  used  by  Professor  Verrill  in  his  papers  in  the 
American  Journal  of  Science.  When  more  than  one  haul  of  the 
dredge  was  made  at  any  of  the  localities,  the  number  of  hauls  is  indi- 
cated in  parenthesis. 


station. 

N.  Lat. 

W. 

Long. 

Depth 
in  filth. 

Nature  of  bottom. 

Temperature.             | 

Air. 

Surface. 

Bottom.* 

a 

41   40 

68 

10 

25 

Soft  sand. 

i 

30 

a         il 

c 

41    25 

66 

45 

28 

Coarse  saud. 

d 

U          il 

66 

24-8 

50 

Sand  and  shells. 

66° 

62° 

45° 

e 

"     " 

65 

58-3 

60 

Shells  and  sand. 

61 

58 

58 

f 

u       a 

65 

50-3 

65 

Dead  shells. 

64 

60 

55 

g 

11       a 

65 

42-3 

430 

Sand,  gravel  and  stones. 

66 

65 

51 

h 

42   56-5 

64 

51-3 

45 

Gravel  and  stones. 

64 

61 

36 

i 

42   44 

64 

36 

60 

Gravel,  stones  and  sponges. 

62 

62 

J 
0(3) 

20 
110 

Mud  and  fine  sand. 
Soft  mud  and  sand. 

56 

49 

42     5 

67 

49 

P 

42     3 

" 

" 

85 

a         u         a         a 

50 

49 

q(^) 

42     0 

67 

42 

45 

Coarse  sand. 

r 

42     3 

67 

31 

40 

a            a 

5(2) 

42   11 

67 

17 

150 

Soft  sandy  mud. 

52 

52 

The  first  dredgings  were  made  on  the  evening  of  August  29,  to  the 
west  of  George's  Shoal,  about  latitude  41°  40'  north,  longitude  68°  10' 


*  Very  little  confidence  can  be  placed  in  these  bottom  temperatures,  as  the  Miller- 
Casella  thermometers  used  did  not  give  uniform  results.  Most  of  the  temperatures 
are  manifestly  much  too  high, 


Smith  and  Harger — St.  George's  Banks.  Dredgings.  3 

west.     The  first  haul,  («),  in  25  fathoms,  soft  sandy  bottom,  gave  the 
following  species : 

Crustacea,  * 

Eupagurus  Bernhardiis  Brandt ;  a1>undant. 
Crangon  'oulgarls  Fabricins  ;  abundant. 
Conilera  poUta  Harger  (Stimpson). 
Epelys  montosus  Smith  (Stimpson). 
Balanus  porcatus  Costa ;  common. 

Annelida. 

(Jistenides  gramdata  Malmgren. 

TURBELLARIA. 

Meckelia  lurida  (?)  Verrill. 

MOLLUSCA. 

JBela  turricuki  (Montagu). 
B.  harptdaria  H.  and  A.  Adams  (Couthouy). 
Buccinwn  tindatum  Linne  ;  very  large  and  abundant. 
Nejitunea pygmoia  H.  and  A.  Adams  (Gould)  ;  abundant. 
Tritia  trlvittata  H.  and  A.  Adams  (Say) ;  abundant. 
Lunatia  heros  H.  and  A.  Adams  (Say). 
L.  hnma.cxdata  H.  and  A.  Adams  (Totten). 
Crepidida plana  Say  {iingniformis  Stimpnon)  ;  several,  living. 
Ensatella  Americana  Verrill  (Gould). 
Modiolaria  nigra  Loven  (Gray). 
Radiata. 

Ee/iinarachnius parma  Gray;  very  abundant. 
Sydractinia  polyclina  Agassiz. 

At  the  second  haul  (^),  in  '^(^  fathoms,  the  bottom  was  of  the  same 
character,  but  a  greater  variety  of  species  was  obtained. 

Crustacea, 

Cancer  irroratus  Say,  young  ;  common. 

Eupagurus  Bernhardus  Brandt;  a)>undant. 

E.  pubescens  Brandt ;  common. 

Crangon  vulgaris  Fabricins  ;  abundant, 
/  Pandahis  annulicornis  Leach  ;  common. 

Stenothoe  peltata  Smith,  sp.  nov.     [Plate  III,  figures  5-8.] 

Fhotis  (?)  sp. 

Ampelisca  sp. 

Xenoclea  megachir  Smith,  sp.  nov,     [Plate  HI,  figures  1-4.] 

Vnciola  irrorata  Say. 

Bulichta  sp. 


4  Smith  and  Harger—St  George's  Banks  Bredgings. 

Annelida. 
Aphrodita  aculeata  Linne. 
Clymenella  torquata  Verrill ;  tubes  only. 

Tu  KBELLARIA. 

Meckelia  lurida  (?)  Verrill. 
M.  ingens  (?)  Leidy. 

MOLLUSCA. 

Bela  turricula  (Montagu). 
B.  harpidaria  H.  and  A.  Adams  (Couthouy). 
Adtnete  viridula  (O.  Fabricius). 
Buccimtm  undatum  Linne  ;  large  and  abundant. 
JSFeptunea  pygmma  H.  and  A.  Adams  (Gould) ;  large  and  common. 
Lunatia  heros  H.  and  A.  Adams  (Say). 
"  "      var.  triseriata  (Say). 

(Jrepidula  plana  Say  {xinguifornds  Stimpson). 
Siliqua  costata  H.  and  A.  Adams  (Say). 

Yoldia  Umatilla  Stimpson  (Say). 
Modiolaria  nigra  Loven  (Gray). 
Farrella  familiaris  Smitt  (Gros)  ;  abundant. 

Gemellaria  loricata  Busk  (Linne). 

Radiata. 

Echinarachnius  parma  Gray  ;  very  abundant. 

Asterias  vulgaris  Stimpson. 

Campanidaria  verticillata  Lamarck  (Linne). 

Sertularia  cupressina  Linne. 

8.  latiusculaf  Stimpson. 

Hydrallmania  falcata  Hincks  (Linne)  ;  abundant. 

Five  successful  hauls  were  made  on  the  line  of  soundings  running 
east  from  George's  Bank,  on  the  parallel  of  41°  25'  north  latitude,  to 
63°  20'  west  longitude.  The  first  of  these  hauls  (c),  beginning  at  the 
western  end  of  the  line,  was  in  about  longitude  66°  45'  west,  from  28 
fathoms,  coarse  sandy  bottom,  September  16.  Here  the  following 
species  occixi-red. 

Crustacea. 

Cancer  irroratus  Say,  young  ;  abundant. 
Eupagurus  Bernhardus  Brandt. 
Crangon  vulgaris  Fabricius ;  common. 
Pandalus  annulicornis  Leach. 
Ampelisca  sp. 

Annelida. 

Nereis  pelagica  Linne. 


Smith  and  Harger — St.  George's  Banks  Dredgings.  5 

TURBELLARIA. 

Meekelia  lurida  (?)  Verrill. 

MOLLUSCA, 

Bela  harpularia  H.  and  A.  Adams  (Coutliouy). 
Tritia  trivittata  H.  and  A.  Adams  (Say) ;  common, 
Lunatia  heros  H.  and  A.  Adams  (Say),  variety  triseriata  ;  common. 
L.  imrnaculata  H.  and  A.  Adams  (Totten). 
Crepidula  fornicata  Lamarck  (Linne) ;  one  dead  specimen. 
Scalaria  Groenlandica  Sowerby. 
Clidiophora  trilineata  Carpenter. 
Mactra  solidissima  Chemnitz  (Gray). 
Astarte  castanea  Say. 

Crenella  glandula  H.  and  A.  Adams  (Totten). 
Ostrea  Virginica  Lister  ;  only  dead  sjjecimens. 
Glandula  arenicola  Verrill ;  abundant. 
Radiata. 

Strongylocentrotus  Drdhachiensis  A.  Agassiz. 
Echinarachnius  2)arma  Gray. 

At  the  second  haul  {d),  longitude  66°  24-8'  west,  50  fathoms,  sandy 
and  shelly  bottom,  August  31,  the  following  species  occuiTed. 

Pycnogonida. 

Nymphon  grossipes  Kroyer. 
Crustacea. 

Cancer  irroratus  Say ;  young. 

Ilyas  coarctatus  Leach  ;  abundant. 

Eupagurus  Bernhardtis  Brandt ;  common. 

E.  Kroyerii  Stimpson;  common. 

E.  ptnhescens  Brandt ;  common. 

Pandalus  annulicornis  Leach  ;  common. 

Vetumnus  serratiis  Goes. 

Melita  dentata  Boeck  ( Gammariis  purpuratus  Stimpson). 

3Icera  Dance,  Bate  (Stimpson)  ;  common. 

Cerapus  rubricornis  Stimpson  ;  common. 

Podocerus  nitidus  Stimpson. 

Unciola  irrorata  Say ;  common. 

Palanus porcatus  Costa;  common. 

AlSTNELIDA. 

Aphrodita  aculeata  Linne. 

Harmothoe  imhricata  Malmgren  (Linne). 

Phyllodoce  catenida  Verrill.     [Plate  IV,  figure  3.] 


6  Smith  and  Harger — St.  George's  Banks  JDredgings. 

Nereis  pelagica  Linne  ;  abundant. 

Cistenides  gramdata  Malmgren. 

Thelepus  cineinnatus  Malmgren  (Fabricius). 

Potamilla  ocidifera  Verrill  (Leidy). 

P.  neglecta  Malmgren. 

Spirorbis  nautiloidesf  Lamarck.     [Plate  IV,  figure  4.] 

Gephyrea, 

PJiascolosoma  cmrnentariuin  Verrill. 

MOLLUSCA. 

Bela  turricula  (Montagu). 

jB.  harpidaria  H.  and  A.  Adams  (Couthouy). 

B.  pleurotomaria  H.  and  A.  Adams  (Couthouy). 

B.  decussata  (Couthouy). 

Neptunea  curta  Verrill  (Jeffreys  sp.  ;  Fasus  Islandicus  Gould). 

N.  decenicostata  (Say). 

N.  pygmo&a  H.  and  A.  Adams  (Gould). 

lAmatia  immaculata  PI.  and  A.  Adams  (Totten). 

Natica  clausa  Broderip  and  Sowerby  ;  common. 

Amauropsis  helicoides  Stimpson  ;  rare. 

Crepidida  plana  Say  [unguiformis  Stimpson). 

Acirsa  horealis  Mon^h  (Beck). 

Margarita  ohscura  Gould  (Couthouy). 

Hanleia  niendicaria  Carpenter  (Mighels  and  Adams). 

Entalis  striolata  Stimpson.     [Plate  I,  figure  3.] 

^olis  sp. 

Thracia  trvncata  Mighels  and  Adams. 

Cyprina  Islandica  Lamarck  (Linne). 

Cardium  pinnulatum  Conrad  ;  abundant. 

Cyclocardia  borealis  Coni-ad  ;  common. 

Astarte  castanea  Say. 

A.  quadrans  Gould. 

Modiolaria  discors  Beck  (Linne). 

Pecten  Islandicus  Chemnitz  (Mtlller). 

Anomia  aculeata  Gmelin  ;   abundant. 

"  "         smooth  variety. 

Boltenia  clavata  Stimpson. 

Pera  crystallina  Verrill  (Moller)  ;  young.     [Plate  VIII,  figure  1.] 
Amaroeciuni  sp. 
Cettidaria  ternata  Johnston  (Busk). 

"  "       var,  duplex  Smitt. 

Caberea  Ellisii  Smitt  (Fleming). 


Smith  and  Marger—St.  George's  Banks  Dredgings.  7 

Bugula  Murrayana  Busk  (Bean) ;  abundant. 
Cellaria  Jistulosa  Liune. 
Biscopora  Skenei  Smitt. 
Cellepora  scabra  Smitt  (Fabricius). 

C.  ramulosa  Linne,  var. ;  with  the  two  last  species  abundant  on 
hydroid  stems. 

Radiata. 

Strongylocentrotus  Brohachiensis  A.  Agassiz. 

Cribrella  sanguinoknta  Liitken. 

Beptasterias  compta  Verrill. 

Ophiopholis  aculeata  Gray ;  common. 

Amphipholis  elegans  Ljungman. 

Ophioglypha  robust  a  Lyman. 

Hydracthiia  polyclina  Agassiz. 

Eudendrium  ramosiwi  Ehrenberg. 

E.  capillar e  Alder  (?) 

Tubularia  indivisa  Linne. 

Gonothyrma  Boveni  AUman. 

Campamdaria  verticdlata  Lamarck  (Linne) ;  common.  * 

C.  Hincksii  Alder. 

G.  voliibilis  Alder  (Linne). 

Bafoea  dumosa  Sars  (Fleming) ;  abundant  on  Bryozoa. 

B.  gracillima  G.  O.  Sars  (Alder) ;  with  last,  common. 

Galycella  syringa  Hincks  (Linne) ;  common. 

Guspidella  humilis  Hincks. 

Haleciuyyi  Beanii  Johnston. 

H.  tenellum  Hincks. 

Sertidarella polyzonias  Gray,  var.  gigantea  Hincks;  common. 

S.  triciispidata  Hincks  (Alder) ;  common. 

Biphasia  fallax  Agassiz  (Johnston) ;  abundant. 

Sertidaria  cupressina  Linne  ;  common. 

S.  latiuscula  Stimpson. 

S.  abietina  Linne. 

Hydrallmania  falcata  Hincks  ;  very  abundant. 

Urticina  crassicornis  Ehrenberg. 

Sponges. 

ThecopJiora  ihla  Wyville  Thompson.     [Plate  VII,  figure  1.] 
Other  undetermined  species. 

At  the  third  haul  (e),  longitude  65"   58-3',  60  fathoms,  shelly  and 
sandy  bottom,  September  16,  the  following  were  found: 


8  Smith  and  Harger — St.  George's  BcmJcs  Bredgings. 

Crustacea. 

Hyas  coarctatus  Leach ;  abundant. 

Eupagurus  Kroyerii  Stimpson  ;  abundant. 

E.  pubescens  Brandt ;  abundant. 

Sabinea  septemcarinata  Owen  ;  one  specimen. 

Pandalus  annulicornis  Leach  ;  common. 

Paramphithoe  pulchella  Bruzelius  (Kroyer). 

Melita  dentata  Boeck  {Gammarus purpuratas  Stmipson). 

Podoceriis  nitidus  Stimpson. 

Caprella  sp. 

Balanus  porcatus  Costa  ;  common. 

Annelida. 

Harmothoe  imbricata  Malmgren. 

Bhynchobolus  capitatus  Verrill  (Oersted  sp.,  not  of  Claparede). 

Thelepus  cincinnatas  Malmgren  (Fabricius). 

Spirorbis  nautiloidesf  Lamarck.     [Plate  IV,  ifigure  4.] 

Gephyrea. 

Phascolosoma  cmmentariutn  Verrill. 

Mollusca. 

Bela  molacea  (Mighels  and  Adams). 
B,  harpularia  H,  and  A.  Adams  (Couthouy). 
Neptunea  curta  Verrill  (Jeftreys  sp.  ;  Fiisus  Islandicus  Gould). 
N.  decemcostata  (Say). 

N'.  pygmcea  H.  and  A.  Adams  (Gould) ;  common. 
iMuatia  heros  H.  and  A.  Adams  (Say),  variety  triseriata. 
Natica  clausa  Brodei'ip  and  Sowerby. 
Amnuropsis  helicoides  Stimpson ;  rare. 
'  Stylifer  Stimpsonii  Verrill;  parasitic  on  Strongylocentrotus  Dr'6- 

bachiensis  A.  Agassiz.     [Plate  I,  figure  1.] 
Aporrhais  occidentalls  Sowerby. 
Acirsa  borealis  Morch  (Beck). 
Margarita  obscura  Gould  (Couthouy)  ;  common. 
Diodora  noachina  Gray  (Linne). 

Hanleia  mendicaria  Carpenter  (Mighels  and  Adams). 
Cylichna  alba  Loven  (Brown). 

Entalis  striolata  Stimpson ;  common.     [Plate  I,  figure  3.] 
Bendronotus  arborescens  Alder  and  Hancock. 
Cyprina  Islandica  Lamarck  (Linne) ;  very  abundant. 
Cardium pinmdattivi  Conrad;  common. 
Astarte  castanea  Say.  « 

A.  quadrans  Gould. 


Smith  and  Harger — St.  George's  Banks  Dredgings.  9 

Astarte  undata  Gould.     [Plate  I,  figures  6-9.] 

Modiolaria  corrugata  Morch  (Stimpson). 

Pecten  tenuicostattis  Mighels. 

P.  Islandicus  Chemnitz  (Miiller). 

Anomia  aculeata  Gmelin,  smooth  variety ;  common. 

Cellularia  ternata  Johnston  (Busk) ;  common. 

JBagula  Murray  ana  Busk  (Bean), 

Gellaria  Jistulosa  Linne. 

Piscopora  Skenei  Smitt,  variety, 

Cellepora  scahra  Smitt  (Fabricius) ;  with  the  last  on  hydrqid  stems, 

Radiata. 

Lophothurla  P\ibricii  Verrill. 
Psolus  phantapus  Oken. 

Strongylocentrotus  Drobachiensis  A.  Agassiz  ;  abundant. 
Echinarachnius  parma  Gray  ;  abundant. 
Crossaster  papposus  Miiller  and  Troschel. 
Crihrella  sanguinolenta  Liltken. 
Hgdractinia  polyclina  Agassiz ;  common. 
Eudendrium  capillare  Akler. 
E.  raniosuni  Ehrenberg. 
Tubularia  indivisa  Linne  ;  common, 
Campanular'ia  iiertlcillata  Lamarck  (Linne) ;  common, 
C.  Hincksii  Alder, 
C.  voluhilis  Alder. 
Gonothyrma  hyalina  Hincks. 
Lafoea  dumosa  Sars  (Fleming) ;  common, 
L.  gracillinia  G.  O.  Sars  (Alder). 
Grammaria  ahietina^  Sars. 

Goppinia  arcta  Hincks  (Dalyell) ;  on  hydroid  stems. 
Sertularella  tricuspidata  Hincks  (Alder) ;  abundant. 
Piphasia  mirabilis  Verrill. 
P.  fallax  Agassiz, 
Serlularia  latiuscida  Stimpson. 
S.  cupressina  Linne. 

Hydrallmania  falcata  Hincks  (Linne) ;  common. 
Epizoantlms  Americanus  Verrill ;  coating  shells  inhabited  by  Eupa- 
gurus  piihescens,  and  also  on  hydroid  stems.    [Plate  VIH,  fig.  2.] 
Urticma  crassicornis  Ehrenlierg. 

At  the  fourth  haul  (/),  longitude  65°  5i)-3',  65  fathoms,  the  bottom 
composed  of  dead  shells,  September  15,  midnight,  the  following 
occurred  : 

Trans.  Conn.  Acad.,  Vol.  III.  2  ,    July,  1873. 


10  Smith  and  Uarger — St.  George's  Banks  Dredgings. 

Crustacea, 

Eupagurus  Kroyerii  Stimpsoii. 
E.  puhescens  Brandt. 
Crangon  vulgaris  Fabricius. 

MOLLUSCA. 

Beta  decussata  (Couthouy). 

Natica  clausa  Broderip  and  Sowerby. 

Stylifer  Stimpsonil  Verrill ;  parasitic  on  Strongylocentrottis  Bro- 
hachiensis  A.  Agassiz.     [Plate  I,  figure  1.] 

Acirsa  borealis  Morch  (Beck). 

Margarita,  ohscnra  Gould  (C?outhouy),  variety. 

Mactra  solidissima  Chemnitz  (Gray);  abundant. 

Cyprina  Islandica  Lamarck  (Linne) ;  common. 

Cyclocardia  borealis  Conrad. 

Astarte  undata  Gould.     [Plate  I,  figures  6-9.] 

Crenella  glandula  H.  and  A.  Adams  (Totten). 
Radiata. 

Strongylocentrotus  Brobachiensis  A.  Agassiz ;  common. 

Echinarachnius  parma  Gray  ;  abundant. 

Hydractinia  polyclina  Agassiz. 

Tubularia  indivisa  Linne. 

Campnnularia  vertieillata  Lamarck  (Linne). 

Sertularella  tricitspidata  Hiiicks  (Alder) ;  common. 

Sertularia  ciipressina  Linne. 

Epizoanthus  Americamis  Verrill ;  coating  shells  inhabited  by  Eupa- 
gurus pubescens.     [Plate  VIII,  figure  2.] 

Urticina  crassicornis  Ehrenbei'g. 

The  fifth  haul  {g)  on  this  line  was  made  on  the  evening  of  Septem- 
ber  15,  to  the  east   of  the   bank,  in   longitude   65°  42*3'  west,  at  a 
depth  of  about  430  fathoms,  on  a  bottom  of  sand,  gravel,  small  and 
large  stones.     Here  the  following  species  occuiTed : 
Pycnogonida. 

Pycnogonum  Uttorale  Mtiller  {pelagicum  Stimpson) ;  common. 

Ckustacea. 

Eupagurus  Kroyerii  Stimpson ;  common. 

Pandalus  annulicornis  Leach ;  several  specimens. 

Thysanopoda  sp,  ;  several  specimens,  perhaps  not  from  the  bottom. 

Unciola  irrorata  Say  ;  several  specimens. 

Melita  dentata  Boeck. 

Scalpelhaii  Stroemi  Sars ;  on  hydroid  stems.     [Plate  III,  fig.  9.] 

Annelida, 

Nothria  conchylega  Malmgren  (Sars) ;  abundant.  [Plate  VII,  fig.  3,] 


Smith  and  Hargei — St.  George's  Banks  Dredgings.  11 

Nephthys  circinata  Yerrill,  sp.  nov. 

Lximbriconereis  frag  His  ffirsted  (Mtiller). 

Leodice  vivida  Verrill  [Eunice  vivida  Stimpson),  [Plate  Y,  fig.  5.] 

Mhynchoholus  capitatus  Verrill  (CErsted  sp.,  not  of  Claparede). 

Gephyrea. 

Phascolosoma  tubicola  Verrill. 

MOLLUSCA. 

Beta  cancellata  (Mighels  and  Adams). 

Neptunea  pygmma  H.  and  A.  Adams  (Gould). 

Z/unatia  Groenlandica  (Mollcr). 

L.  immaculata  H.  and  A.  Adams  (Totten). 

Natica  clausa  Broderip  and  Sowerby. 

Margarita  ohscura  Gould  (Couthouy). 

Diodora  noachina  Gray   (Tjinne),  variety  princep)s   (Mighels  and 

Adams). 
Entails  striolata  Stimpson.     [Plate  I,  figure  3.] 
Astarte  lens  Stimpson  ;  dvv^arf  variety. 
Cryptodon  obesns  Verrill.     [Plate  I,  figure  11.] 
Pecten  pustulosiis  Verrill. 

Vescictdaria  armata  Verrill ;  on  Sertularia  argentea. 
Several  other  species  of  Bryozoa. 

Radiata. 

Lopthothuria  squamata,  Verrill. 

Pentaeta  asshnills  (Duben  and  Koren). 

Schizaster  fragilis  Agassiz  (Duben  and  Koren). 

Strong ylocentrot as  Probac/iiensis  A.  Agassiz  ;  several. 

Echinarac/mixs  p((riiia  Gray  ;  common. 

Ophioglypha  Sarsii  Lyman  ;  common. 

Eudendritim  ramosuvi  Ehrenberg  (Linne). 

Tubidaria  indivisa  Linne. 

Campanularia  virticillata  Lamarck  (Linne). 

Lafoea  graclUhna  G.  O.  Sars  (Alder). 

Calycella  producta  G.  O.  Sars. 

Halecinm  robustuui  Vei-rill. 

Sertularella  Gayi  Hincks  (Lamoroux). 

S.  triciispidata  Ilincks  (Aldei-)  ;  with  reproductive  capsules. 

Sertularia    argentea   Linne,    slender   variety;    with    reproductive 

capsules. 
Epizoanthus  Americanus  Verrill  ;  upon  small  stones. 
Urticina  crassicornis  Erhenberg  ;  young  specimens. 
U.  nodosa  Verrill  (Fabricius) ;  two  large  specimens. 


12  Smitfi  and  Harger — St.  George's  Banks  Dreclgmgs. 

On  the  line  of  soundings  from  near  Cape  Sable,  Nova  Scotia,  to  lati- 
tude 41°  25'  north,  longitude  63°  20'  west,  two  successful  hauls  were 
made  September  12,  on  Le  Have  Bank.  The  first  (A),  latitude  42°  56-5' 
north,  longitude  64°  51 '3'  west,  45  fathoms,  gravelly  and  stony  bot- 
tom, gave  the  following  species  : 

Crustacea. 

Hyas  coarctatus  Leach  ;  very  abundant. 

Eupagurus  Kroyerii  Stimpson  ;  abundant. 

Hippolyte  spina  Leach  ;  several  specimens. 

a.  pusiola  Kroyer.  ^ 

Syrrhoe  crenulata  Goes  ;  a  single  specimen. 

Tiron  acanthurus  Lilljeborg  ;  one  specimen. 

Paramphitho'e  cataphracta  Smith  (Stimpson). 

Tritropis  aculeata  Boeck,  and  several  undetermined  Amphipods. 

Annelida  and  Gephyrea. 

Nychia  cirrosa  Malmgren  (Pallas). 

Eunod  nodosa  Malmgren  (Sars). 

JELarmothoe  imhricata  Malmgren  (Linne). 

Nereis  pelagica  Linne  ;  abundant. 

Nothria  conchylega  Malmgren  (Sars) ;  very  abundant.    [Plate  VII, 

figure  3.] 
Spiocluetopterus  (?) ;  tubes  only. 
Cistenides  granulala  Malmgren, 
Thelepus  cincinnatus  Malmgren  (Fabricius). 
Potamilla  ocidifera  Verrill  (Leidy). 
P.  neglecta  Malmgren  ;  very  abundant. 
Spirorhis  valida,  Verrill,  sp.  nov. 
S.  hicidus  Morch. 
Phascolosoma  ccementarium  Verrill. 

TURBELLARIA. 

Leptoplana  ellipsoides  Girard. 

MOLLUSCA. 

Bela  violacea  (Mighels  and  Adams). 

Admete  viridula  Stimpson  (O.  Fabricius). 

Buccinunn  undatwm  Linne ;  common. 

Neptunea  deeemcostata  (Say). 

N.  pygmoea  H.  and  A.  Adams  (Gould)  ;  common. 

Trophon  Gnvneri  Loven  ;  three  sjDecimens. 

Lunatia  Groenkwdica.  (Moller). 

Natica  clausa  Broderip  and  Sowerby ;  abundant. 

Grepidula plana  Say  {unguiformis  Stimpson);  one  alive. 

TVichotropis  horealis  Sowerby;  abundant. 


Smith  and  Harger — Sf.  George's  £anks  Dredgings.  13 

Aporrhais  occidentalls  Sowerby. 

Turritella  erosa  Couthoiiy ;  common. 

Scalaria  Groerdandica  Sowerby  ;  abuudant. 

Margarita  cinerea  Gould  ;  common. 

M.  Groenlandica  Moller  {M.  undulata  Gould). 

Trachydermon  album  Carpenter  (Montagu). 

Entails  striolata  Stimpson;  abundant.     [Plate  I,  figure  3.] 

Dendronotus  arhoreseens  Alder  and  Hancock. 

Mya,  truncata  Linne. 

Cardiian  pinnulaturn  Conrad ;  common. 

Cyclocardia  N'ovanglim  Morse  ;  common. 

Astarte  elliptica  (Brown);  very  abundant.     [Plate  I,  figure  10.] 
A.  Banksii  Leach;  common.     [Plate  I,  figure  12.] 
A.  undata  Gould  ;  common.     [Plate  I,  figures  6-9.] 
Pecten  Islaudicus  Chemnitz  (Mtiller) ;  abundant. 
Boltenia  Molteni. 

Cynthia  carnea  Verrill. 

Terehrattdina  sep)tentrionalis  (Couthouy) ;  common. 
Mhynchonella  psittacea  (Gmelm). 
Myriozoum  coaretatam  Smitt  (Sars) ;  common. 
Eschara  papposa  Packard. 
Escharoides  rosacea  Smitt. 

Cellepora  avicidaris  Hincks. 
Radiata. 

Lophothuria  Fahricii  Verrill. 

Strongylocentrotus  Drobachlensis  A.  Agassiz;  common. 

Grossaster  papposus  Mtiller  and  Troschel;  young. 
Pteraster  milltaris  Mtiller  and  Troschel. 

OphiophoUs  acideata  Gray  ;  common. 

Ophioglypha  Sarsii  Lyman. 

0.  robusta  Lyman. 

Clytia  Johnstoni  Hincks  (Alder). 
Hydractinia  polyclina  Agassiz ;  abundant. 
Eudendriunti  cappilare  Alder. 

Tubidaria  indivisa  Linn^ ;  common. 

Cainpanularia  verticillata  Lamarck  (Linn6). 

C.  IIi7icksii  Alder. 

Lafoea  graclllhna  G.  O.  Sars. 

Calycella  syringa  Hincks  (Linne). 

Sertularella  tricuspidata  Hincks  (Alder);  common. 

S.  polyzonias  Gray,  variety  gigantea  Hincks. 

Thuiaria  articulata  Fleming  (Pallas). 

Urticina  crassicornis  Ehrenberg  ;  abundant. 


14  Smith  and  Jffarger — St.  George's  Banks  Dredgings. 

At  the  second  haul  [i),  latitude  41°  44'  north,  longitude  64°  36' 
west,  60  fathoms,  coarse  gravel,  stones,  and  sponges,  the  following 
occurred : 

Pycnogonida. 

Nymphon  grossipes  Kroyer, 

Crustacea. 

Hyas  coarctatus  Leach. 

H.  araneus  Leach. 

Eupagurus  Kroyerii  Stimpsou  ;  abundant. 

Sabinea  septemcarinata  Owen;  two  specimens. 

Tritropis  aculeata  Boeck. 

Acanthozone  cuspidata  Boeck. 

Annelida. 

Eunoa  nodosa  Malragren  (Sars). 

Harmothoe  imhricata  Malmgren  (Linne). 

Lagisca  rarispina  Malmgren  (Sars). 

Nothria  conchylega  Malmgren  (Sars) ;  abundant.   [Plate  VII, fig.  3.] 

Thelepiis  cinclnnatus  Malmgren  (Fabricius). 

I*otamUla  neglecta  M'dlmgYQn  ;  abundant. 

Spirorhis  valida  VeiTill. 

MOLLUSCA. 

Adrnete  viridula  Stimpson  (O.  Fabricius) ;  common, 

Trophon  Gunneri  Loven. 

Natica  clausa  Broderip  and  Sowerby. 

Aporrhais  occidentalis  Sowei'by. 

Turritella  reticulata  Mighels  and  Adams. 

Margarita  cinerea  Gould. 

Hanleia  mendicaria  Carpenter  (JVlighels  and  Adams). 

Trachydermon  album  Carpenter  (Montagu). 

Entalis  striolata  Stimpson  ;  abundant. 

uEolis  rufibranc.hialis  Alder  and  Hancock  (?). 

Cardium  pinmdatum  Conrad. 

Terebratulina  septentrionalis  (Couthouy) ;  common. 

Atnarcecium  glabrum  Verrill. 

Discopora  Skefiei  Smitt. 

Radiata. 

Gribrella  sanguinolenta  Liitken. 
Ophiopholis  aculeata  Gray  ;  abundant. 
Ophioglypha  Sarsii  Lyman. 
Lafoea  gracillima  G.  O.  Sars. 
Sertularella  tricuspidata  Hincks. 


Smith  and  Harger — St.  George's  Bmiks  Dredgings.  15 

Sertularella  polyzoiiias  Gray,  variety  gigantea  Hincks. 
Hydrallmania  falcata  Hincks,  var.  tenerrima  (Stimpson). 
Aglaophenia  myriophylhdn  Laraoroux  (Linne), 
Granimaria  abietina  Sars. 

Many  species  of  sponges  were  also  obtained,  but  most  of  them  are 
as  yet  undetermined.    Among  them  is  Thecophora  ibla  W.  Thompson. 

On  leaving  Halifax,  N.  S.,  September  11,  one  haul   (j/)   was  made 
just  off  Chebucto  Head,  in  20  fathoms,  soft  mud  and  fine  sand  with 
decaying  seaweed.     Here  the  following  were  found: 
Crustacea. 

Hyas  araneus  Leach ;  common. 

Eupagtiriis  pubescens  Brandt. 

Diastylis  quadrispinosa  G.  O.  Sars ;  common. 

D.  sculpta  G.  O.  Sars. 

Halii-ages  fidvocinctus  Boeck  (Sars). 

Gammarus  ornatus  Edwards ;  perhaps  from  floating  sea-weed. 

Ampelisca  sp. ;  common. 

MonoGxdodes  borealis  Boeck. 

Annelida. 

Harmothoe  imbricata  Malmgren  (Linn6). 

Goniada  maculata  OErsted. 

Brada  sp. 

Cistenides  granulata  Malmgren. 

Mollusca. 

Aporrhais  occidentcdis  Sowerby;  common. 

Turritella  reticulata  Mighels  and  Adams  ;  common. 

Margarita  varicosa  IMighels  and  Adams ;  common. 

M.  obscura  Gould  (C'outhouy),  variety. 

Thracia  niyopsis  Beck. 

Macoma proxima  (Gray). 

Astarte  elliptica  (Brown).     [Plate  I,  figure  10.] 

Anomia  aculeata  Gmelin. 

Terebratidina  septentrioualis  (Couthouy). 

Rhynchonella  psittacea  (Gmelin). 

Grisia  eburnea  Lamoroux  (Linne).     [Plate  II,  figures  3-4.] 

F lustra  papyrea  (Pallas). 

Radiata. 

Ophiopholis  aculeata  Gray. 
Ophioglypha  robusta  Lyman. 
Manania  auricula  Clark  (?) 
Hydrallmania  falcata  Hincks  (Linne). 


16  Smith  and  Han/er — St.  George's  Hanks  Dredgings. 

The  dredging  while  Dr.  Packard  and  Mr.  Cooke  were  on  board  the 
Bache  was  at  five  localities.  First  (o),  just  on  the  northwestern  bor- 
der of  George's  Bank,  latitude  42°  5'  north,  longitude  67°  49'  west, 
in  110  fathoms,  three  hauls  were  made  from  a  bottom  of  soft  sandy 
mud  with  a  few  stones,  and  the  following  collected  : 
Crustacea. 

Caridion  Gordonl  Goes ;  one  small  specimen. 

Ilarpina  fusiformis  (Stimpson) ;  common. 

Stegocephalus  ampulla  Bell ;  one  large  specimen. 

Unciola  irrorata  Say  ;  common. 

Anthura  brachiata  Stimpson. 

Annelida. 

Lmnillaf  mollis  G.  O.  Sars. 

Pholoe  mimita  Malmgren. 

Nephthys  ciliata  Malmgren  (Miiller).     [Plate  V,  figure  1.] 

N.  ingens  Stimpson. 

Phyllodoce  sp. 

Eteone  depressa  jNIalmgren  (?). 

Nereis  pelagica  Linne  ;  common. 

Lumbriconereis  fragilis  Oersted  (Mtiller).     [Plate  V,  figure  2.] 

Ninoe  nigripes  Verrill.     [Plate  V,  figure  3.] 

Leodice  vivida  Verrill  (Stimpson).     [Plate  V,  figure  5.] 

Nothria  coiwhylega  Malmgren  (Sars).     [Plate  VII,  figure  3.] 

N.  opalina  Verrill ;  common.     [Plate  VII,  figure  4.] 

Goniada  maculata  CErsted. 

Rhynchoholus  capitatus  Verrill  (CErsted  sp.,  not  of  Claparede). 

Ammotrypane  fimhriata  Verrill. " 

Eamenia  crassa  CErsted. 

Trophonia  aspera  Verrill  (Stimpson). 

Sternaspis  fossor  Stimpson. 

Scolecolepis  cirrata  Malmgren  (Sars). 

Nbtom,asti(S  latericins  Sars. 

Ancistria  capillaris  Verrill. 

Maldane  Sarsii  Malmgren. 

Rhodine  Zioveni  Malmgren. 

Nicomache  lumhrlcalis  Malmgren  (Fabriciusj. 

Axiothea  catenata  Malmgren  (?). 

Praxilla  pnetermissa  Malmgren. 

P.  gracilis  Malmgren. 

P.  species  undetermined. 

Am.m,ochares  assimilis  Sars.     [Plate  V,  figure  4.] 

Ampharete  arctiea  Malmgren. 


Smith  and  Harger — St.  George's  Banks  Bredgings.  V 

Ampharete  Finrnarchira  (?)  Malmgren  (Sars). 

A.  gracilis  Malmgren. 

Amphicteis  Gunneri  Malmgren  (Sars)  ;  abundant. 

Samytha  sexcirrata  Malmgren  (Sars). 

Samythella  elongata  Verrill. 

Melinna  cristata  Malmgren  (Sars.) 

Amphitrite  cirrata  Miiller. 

Pista  cristata  Malmgren  (Mtiller).     [Plate  IV,  figure  2.] 

Grymma  spiralis  Verrill.     [Plate  IV,  figure  1.] 

Terebellides  Stroemi  Sars. 

Polycirrus  sp. 

Sahella  pavonia  (?)  Malmgren. 

Fotamilla  neglecta  Malmgren. 

Protxda  media  Stimpson ;  tubes  only.     [Plate  VI.] 

P.  horealis  (?)  Sars ;  tubes  only. 

Gephyrea. 

Phascolosoma  cmmentarium  Verrill. 

P.  boreale  Keferstein  (?) 

P.  tuhicola  Verrill. 

Chcetoderma  nitidulitm  Loven,     [Plate  VIII,  figures  3-4.] 

TURBELLARIA. 

Meckelia  lurida  (?)  Verrill. 

MOLLUSCA. 

Pleurotoniella  Packardii  Verrill ;  one  living. 
Adniete  viridula  Stimj^son  (O.  Fabricius). 
JVeptunea  pygmcea  H.  and  A.  Adams  (Gould) ;  common. 
Ringicula  nitida  Verrill.     [Plate  I,  figure  2.] 
Lunatia  Groenlandica  (Mollei'). 
Natica  clausa  Broderip  and  Sowerby. 
Velutina  Icevigata  (Linne). 
Margarita  citterea  Gould. 
Lepeta,  cmca  Mtiller. 

Trachydermon  alburn  Carpenter  (Montagu). 
Cyliclina  alba  Loven  (Brown). 
Philine  s]>. 

Entalis  striolata  Stimpson  ;  common. 
JVecera  arctiea  Sars. 
Thracia  myopsis  Beck. 
Macoma  proxinta  (Gray). 
Gardiuni  pinnidatum  Conrad. 
Astarte  lens  Stimpson,  d^varf  var. ;  common. 
Teans.  Conn.  Acad.,  Vol.  ITI.  3  August,  1874. 


18  Smith  and  Harger — St.  George's  Banks  Dredging s. 

Cryptodon  Gouldii  H.  and  A.  Adams  (Pliilippi). 
Yoldia  obesa  Stimpson. 

Leda  tenuisulcata  Stimpson  (Couthouy)  ;  common. 
(Jrenella  glandula  H.  and  A.  Adams  (Totten), 
Pecten  Ishindlcus  Chemnitz  (Mullei"). 
P.  tenuicostatus  Mighels. 
Aiioniia  acideata  Gmelin. 
Ascldiopsis  complanata  Verrill  (Fabricius). 
TerebratuUna  septentrionalis  (Couthouy). 
Dtscofascigera  lucernaria  Sars. 
Cellularia  sp. 

Bugula  avicularia  Busk,  v a.viet  j  /astigiata. 
Radiata. 

Lophothuria  Fabricii  Verrill. 

Pentacta  assimilis  (Duben  and  Koren). 

Thyone  scabra  Verrill. 

Schizaster  fragilis  Agassiz  (Duben  and  Koren) ;  several. 

Ctenodiscus  crispatus  Duben  and  Koren. 

Ophioglypha  affinis  Lyman. 

0.  Sarsii  Lyman. 

Opiopholis  aculeata  Gray. 

Ophiacantha  spimdosa  Mtlller  and  Troschel. 

Archaster  arcticus  Sars. 

Pennatida  acideata  Danielsen. 

Gerianthus  borealis  Verrill.     [l^late  11,  figure  5.] 

Second  (jo),  a  little  to  the  southeast  of  the  first,  latitude  42°  3',  lon- 
gitude 67°  49',  85  fathoms,  one  haul  from  a  bottom  of  the  same  char- 
acter as  at  first  locality  : 
Crustacea. 

Harpina.  fusiformis  Smith  (Stimpsoji) ;  common. 

Aknelida. 

Antinoe  Sarsii  Kinberg. 

Neplithys  ingens  Stimpson. 

N.  circinata  Verrill,  sp.  nov. 

Lmnbriconereis  fragilis  (Ersted  (Miiller).     [Plate  V,  figure  2.] 

Nothria  eonchylega  Malmgren  (Sars).     [Plate  VII,  figure  3.] 

^4  rn  mo  try  pane  firnbriata  Ve  rr  il  1 . 

JEmnenia  crassa  Oersted. 

Trophonia  aspera  Verrill  (Stimpson). 

Sternaspis  fossor  Stimpson. 

Ghoetozone  setosa   Malmgren. 


Smith  and  Harger — St.  George's  Banks  Dredgings.  1 9 

Ancistria  capillaris  Verrill. 
Maldane  Sarsii  Malmgren. 
Mhodine  Loveni  Malmgren. 
Pr axilla  praetermissa  Malmgren. 
Anmiochares  assiniilis  Sars. 
Ampharete  (irctica  Malmgren. 
Ainphirteis  Sundevalli  Malmgren. 
Terehellides  Stroetni  Sars. 
Polycirrus  sp. 

Gepuyrea. 

Phascolosoma  cmmentarium  Verrill. 

MOLLUSCA. 

Natica  clausa  Broderip  and  Sowerby. 
Scalar  la  Grcenlandlc<i  Sowerby. 
Yoldia  obesa  Stimpson. 
Y.  thraciformis  Stim))Son  (Storer). 
Radiata. 

Schizaster  fragiUs  Agassiz  (l)uben  and  Koren). 
Edwardsia  sp. 

Third  (</),  still  farther  to  the  southeast,  latitude  42°,  longitude  67° 
42',  two  hauls  in  45  fathoms,  coarse  sandy  bottom : 

Crustacea. 

Hyas  coarctatus  Leach  ;  very  abundant. 
Cancer  Irroratus  Say  ;  one  young  specimen. 
Eupagurus  Bernhardus  Brandt. 
E.  Kroyeri  Stimpson  ;  common. 
E.  puhescens  Brandt ;  common. 
Crangon  vulgaris  Fabricius  ;  abundant. 
Hippolyte  pusiola  Kroyer. 
Pandalus  annidicomls  Leach  ;  common. 
Vertin)i7iKS  serratus  Goes. 
Paramphithoe  cataphracta.  Smith  (Stimpson). 
P.  pnlchella  Bruzelius. 
Phoxus  Kroyeri  Stimpson. 
Melita  dentata  Boeck, 

Pontogeneia  inermis  Boeck  ;  one  specimen. 
Gerapus  rubricornis  Stimpson. 

Xenoclea  rnegachir  Smith,  sp.  nov.     [Plate  III,  figures  1-4.] 
JJnciola  irrorata  Say. 
Balanus  porcatus  Costa. 


20  Smith  ayxd  Harger — St.  George's  Banks  Dredgings. 

Annelida. 

Harmothoe  imhricata   Malmgren. 

JOagisca  propinqua  Malmgren. 

Eusyllis  phosphorea  Verrill,  sp.  nov.     [Plate  VII,  figure  2.] 

Nereis  pelagica  Linne. 

Leodice  vivida  Verrill  (Stimpson).     [Plate  V,  figure  5.] 

Nothria  conchylega  Malmgren  (Sars).     [Plate  VII,  figure  3. J 

Am7noehares  assirtdlis  Sars.     [Plate  V,  figure  4.] 

Amphitrite  Groenlandica  Malmgren. 

Thelepus  cincinnatus  Malmgren  (Fal)ricius). 

Chone  infundibidiformis  Kroyer. 

Spirorhis  nautiloides  Lamarck  ? 

MOLLUSCA. 

Hela  harpularia  H.  and  A.  Adams  (Couthouy). 
B.  pleuroto)7iaria  H.  and  A.  Adams  (Couthouy). 
JB.  turricida  (Montagu). 
Buccimim  utidatum  Linne. 

Neptunea  curta  Verrill  (Jeffreys  sp.,  Fusus  Islatulicus  Gould). 
N.  pygmoea  H.  and  A.  Adams  (Gould). 
Lunatia  heros  H.  and  A.  Adams,  variety  triserlata  (Say). 
L.  immaculata  H.  and  A.  Adams  (Totten). 
Turritella  erosa  Couthouy, 
T.  acicula  Stimpson. 

Margarita  obscura  Gould  (Couthouy) ;  common. 
Diodora  noachina  Gray  (Linne). 
Hauleia  mendicaria  Cai-penter ;  large  specimens. 
Mactra  so^^V?^ss^m a  Chemnitz  (Gray). 
Gyprina  Islandiea  Lamarck  (Linne). 
Gardium  pinnulatnm  Conrad  ;  common. 
Astarte  quadrans  Gould. 

Leda  tenuisidcata  Stimpson  (Couthouy) ;  common. 
Grenella  glandida  H.  and  A.  Adams  (Totten). 
Modiola  modiolus  Turton  (Linne). 
Modiolaria  Imvigata  (Gi-ay). 
Pecten  tenuicostatus  Mighels. 
P.  Islandicus  Chemnitz  (Mtiller). 
Anomia  aculeata  Gmelin. 
Glandula  arenicola  Verrill. 
Gellularla  ternata  Johnston  (Busk). 
Gemellaria  loricata  Busk  (Linne). 
Bugula  Murray  ana  Busk  (Bean). 
Cellepora  tuberosa  D'Orhigny. 


Smith  and  Harger — St.  George's  Banks  Dredgings.  21 

Kadiata. 

Lophothuria  Fabricii  Verrill, 

Strongylocentrotus  Drbhachiensis  A.  Agassiz  ;  common. 
Ecliinarachnius  parma  Gray  ;  very  abundant. 
Solaster  endeca  Forbes. 
Crossaster  papposus  Mtiller  and  Troschel. 
Crihrella  sanguhiolenta  Liitken. 
Asterias  mdgaris  Stimpson. 
Leptasterias  Stimpsoni  Verrill. 
OphiophoUs  acideata  Gray ;  common. 
Ophioglypha  robusta  Lyman. 
Eudendriuni  rarnosum  Ehrenberg  (Linne). 
E.  capillare  Alder. 

Campanularia  verticillata  Lamarck  ;  common. 
C.  Hincksii  Alder. 

Lafoea  dumosa  Sars  (Fleming)  ;  common. 
Calycella  syringa  Hincks  (Linne). 
Grammaria  ahictina  Sars  {G.  robusta  Stimpson). 
Coppinia  arcta  Hincks  ;  on  hydroid  stems. 
Halecium  labrosum  Alder. 

Sertularella polyzonias  Gray  (Linne) ;  common. 
"  "         variety  gigantea  Hincks. 

S.  tricvspidota  Hincks  (Alder) ;  abundant. 
Sertularia  abietina  Linne;  one,  very  large. 
S.  latiuscula  Stimpson. 
S.  cupressina  Linne  ;  common. 

S.  argentea  Ellis  and  Solander.     [Plate  HI,  figure  2.] 
Hydvallmania  fidcata  Hincks;  abundant. 

Third  (r),  north  and  a  little  east  of  the  last,  latitude  42°  3',  longi- 
tude 67°  31',  in  40  fathoms,  coarse  sandy  bottom: 

Crustacea. 

Eupagnrus  Bemhardns  Brandt. 

Annelida. 

Dodecaceria  concharum  CErsted. 
Spirorbis  quadrangidaris  Stimpson. 

MOLLUSCA. 

Bela  harpidaria  H.  and  A.  Adams  (Couthouy). 
Natica  clausa  Broderip  and  Sowei-by. 
Scalaria  Groenlandica  Sowerby. 
Margarita  obsciira  Gould  (Couthouy). 
Mactra  solidissima  Chemnitz  (Gray). 


22  Smith  and  Harger — 8t.  George's  JBanhs  Dredgings. 

Cyprina  Islandica  Lamarck  (Ijinne). 

Cardiwrn  pinnulatum  Conrad. 

Astarte  castanea  Say. 

Pecten  temdcostatus  Migliels. 

Cellularia  sp. 

Bugula  Murrayana  Busk  (Bean). 

Radiata. 

Echinarachnms  parma  Gray. 

Hydractinia  polyclina  Agassiz. 

Sertularella  polyzonias  Gray,  var.  gigantea  Hincks. 

Sponges. 

Ghalina  oculata  Bowerbank,  and  a  massive  siliceous  sponge. 

Fifth  {s)  a  little  to  northeast  of  the  bank,  latitude  42°  11',  longi- 
tude 67°  iV,  two  hauls  in  150  fathoms,  soft  sandy  mud  with  a  few 
pebbles : 

Crustacea. 

Hyas  coarctatus  Leach. 
Eupagurus  Bernhardus  Brandt. 
E.  Kroyeri  Stimpson. 
E.  puhescens  Brandt. 
Ptilocheirus  pingxiis  Stimpson. 
JEga  psora  Bate  and  Westwood. 
Conilera polita  Harger  (Stimpson). 
JBalanus  porcatus  Costa. 

Annelida. 

LcBtraonice filicornis  Kinberg. 

Harmothoe  imbricata  Malmgren  (Linne). 

Antinoe  angusta  Verrill,  sp.  nov. 

Eucranta  villosa  Malmgren. 

Nepthys  ingens  Stimpson. 

Eumbrieonereis /ragllis  CErsted  (Miiller).     [Plate  V,  figure  2.] 

Nothria  conchylega  Malmgren  (Sars).     [Plate  VII,  figure  3.] 

N',  opalina  Verrill.     [Plate  VII,  figure  4.] 

Goniada  maculata  Ql^i'sted. 

Scalihregma  inflation  Rathke. 

Spiochcetopterus  (?) ;  tubes  exactly  like  those  of  this  genus. 

Scolecolepis  cirrata  Malmgren  (Sars). 

Ancistria  capillaris  Verrill. 

Maldane  Sarsii  Malmgren  ;  abundant. 


Smith  and  Sarger — St.  George's  Banks  Dredging s.  23 

Cistenides  granulata  Malmgren. 

Amphicteis  Gunneri  Malmgren  (Sars). 

Amage  auricula  Malmgren. 

Smythella  elongata  Verrill. 

Melinna  cristata  Malmgren  (Sars). 

Pista  cristata  Malmgren  (Sars).     [Plate  IV,  figure  2.] 

Grymcea  spiralis  Verrill.     [Plate  IV,  figure  1.] 

Terebellides  Stroemi  Sars. 

Protula  borealis  Sars  ?  ;  tubes  only. 

Gephyrea. 

PhasGolosoma  cmmentariutn  Verrill. 
P.  boreale  Keferstein  (?) 
P.  tubicola  Verrill. 

MOLLUSCA. 

Adniete  viridula  Stimpson  (Miiller). 

Neptunea  pygmoia  H.  and  A.  Adams  (Gould) ;  abundant. 
Ringicida  nitida  Verrill ;  one  living.     [Plate  I,  figure  2.] 
Lunatia  Grmnlandica  (M  oiler). 
Natica  clausa  Broderip  and  Sowerby. 
Veliitina  zonata  Gould. 
Torrellia  vestita  Jeffreys  ;  one  specimen. 
Aporrhais  occidentalis  Sowerby. 
Margarita  cirierea  Gould. 
M.  obscura  Gould  (Couthouy). 
Trachydermon  album  Carpenter. 

Scaphander  puncto-striatus  Stimpson  ;  one  very  large. 
Gylichna  alha  Loven  (Brown). 

Entalis  striolata  Stimpson  ;  abundant.     [Plate  I,  figure  ;^.] 
Dentalium  occidentale  Stim})son  ;  one  specimen. 
Nemra  arctica  Sars 
Thracia  myopsis  Beck. 
Cardium  pinmdatum  Conrad. 
Astarte  quadrans  Gould. 
A.  lens  Stimpson,  dwarf  variety  ;  common. 
Yoldia  obesa  Stimpson. 
Deda  tenuisulcata  Stimpson  (Couthouy). 
Area  peetunculoides  Scacchi ;  several. 
Pecten  pustulosus  Verrill  ;  one  living. 
Anomia  aculeata  Gmelin. 
Glandula  arenicokt  Verrill ;  common. 
Terebratulina  septentriorialis  (Couthouy) ;  abundant. 


24  Smith  and  Harger — St.  George's  Banks  Dredgings. 

Hornerea  lichenoides  Smitt  (Linne). 
Discoporella  verrucaria  Smitt, 

Gellularia  ternata  Johnston,  var.  gracilis  {arctica  Busk  sp.). 
G.  Peachii  Busk. 
Gcd)erea  Ellisii  Smitt  (F'leming). 
JBugula  Murray  ana  Busk  (Bean)  ;  abundant. 
jB.  avicularia  Busk,  var.  fastigiata. 
Gellepora  scahra  Smitt  (Fabricius). 
G.  ramulosa  (Linne). 

Radiata. 

Thyone  scahra  Verrill. 

Schizaster  fragilis  Agassiz  (Duben  and  Koren)  ;  several. 

Echinarachnius  parina  "Gray. 

Solaster  furcifer  Duben  and  Koren  ;  one  specimen. 

Archaster  arcticus  Sars  ;  one  specimen. 

Ophioglypha  Sarsii  Lyman. 

O.  affinis  Lyman. 

Ophiacantha  spinxdosa  Milller  and  Troschel. 

Glytia  Johnstoni  Hincks. 

Eudendrium  capillar e  Alder. 

Sertularella  tricuspidata  Hincks  (Alder). 

S.  Gayi  Hincks  (Lamoroux). 

Sertularia  cnpressina  Linne. 

Pennatula  aculeata  Danielsen. 

Virgidaria  Lyungmanii  KoUiker. 

Bolocera  Tuedice  Gosse  ;  tentacles  only. 

Urticina  crassicornis  Ebrenberg. 

GeHanthus  borealis  Verrill.     [Plate  II,  figure  5.] 

The  lists  of  species  from  all  the  localities  (a,  5,  c,  d,  e,  /',  q,  r,)  on 
George's  Bank  itself,  show  that  tlie  fauna  of  that  region  is  almost 
exactly  the  same  as  in  the  Bay  of  Fundy,  at  the  same  de))ths  and  on 
similar  bottom.  To  be  sure,  on  the  one  hand,  several  arctic  species, 
not  yet  found  in  the  Bay  of  Fundy,  occurred  upon  the  Bank  ;  but  on 
the  other  hand,  several  apparently  more  southern  forms  were  found, 
as  the  species  of  Grepidxda  and  Stylifer.  The  two  dredgings  {h 
and  i)  upon  LeHave  Bank  seem  to  indicate,  as  we  might  expect,  a 
somewhat  more  arctic  fauna  than  that  upon  George's  Bank,  since 
several  arctic  species,  not  known  from  George's  Bank  or  the  Bay  of 
Fundy,  occurred  there,  though  Grepidula  phiita  was  also  found. 

The  dredgings  in  deep  water  near  the  Banks  indicate  a  fauna  quite 
different  from  that  upon  the  Banks  themselves.     This  is  undoubtedly 


Smith  and  Uarger — St.  George's  Banhs  Dredgings.  25 

partially  owing  to  the  diiference  in  the  character  of  the  bottom  as 
well  as  to  the  diiference  in  depth.  Of  the  species  occurring  in  deep 
water,  a  much  larger  proportion  than  in  the  shallower  waters  are  the 
same  as  those  of  northern  Europe,  At  the  greatest  depth  reached 
by  the  dredge,  about  430  fathoms,  at  the  locality  [g)  east  of  George's 
Bank,  almost  all  the  species  which  were  not  also  found  in  shallow 
water  are  European.  Some  of  these  species,  however,  were  dredged 
in  1872,  by  Prof.  Veri-ill,  in  the  central  part  of  the  Bay  of  Fundy, 
east  of  Grand  Menan  Island,  in  95  to  106  fathoms,  where  the  char- 
acter of  the  bottom  was  quite  similar  to  that  of  our  deepest  dredg- 
ing. 

At  each  of  the  three  deepest  of  Dr.  Packard's  dredgings,  (o)  110 
fathoms,  {p)  85  fathoms,  and  (s)  150  fathoms,  the  bottom  was  com- 
posed of  soft  sandy  mud,  very  ditferent  in  character  from  that  at  any 
of  the  localities  examined  by  us.  The  fauna  of  the  bottom  at  these 
three  places  was  essentially  the  same,  and,  although  many  of  the 
species,  on  account  of  the  character  of  the  bottom,  were  diiferent 
from  those  at  the  locality  in  430  fatlioms,  about  the  same  proportion 
are  identical  with  European  species. 

Although  the  dredgings  in  deep  water  were  so  few,  the  facts  pre- 
sented in  the  foregoing  lists  with  reference  to  the  bathymetrical  dis- 
tribution of  species,  are  important  and  very  interesting.  Of  the 
species  enumerated  from  430  fathoms,  considerably  more  than  half 
are  well  known  shallow  water  forms,  many  of  them  even  occurring 
between  tides  in  the  Bay  of  Fundy  and  at  other  points  on  the  coast, 
while  nearly  all  the  species  mentioned  are  also  found  at  less  than  50 
fathoms  depth.  The  same  remarks  Avill  apply  to  the  deeper  dredg- 
ings of  Dr.  Packard  and  Mr.  Cooke.  The  species  from  the  deepest 
dredging  belong  apparently  to  as  highly  organized  groups  of  animals 
as  do  those  from  shallow  water.  We  were  not  able  to  detect  any 
decrease  in  the  intensity  of  the  colors  in  individuals  from  this  depth. 
The  colors  of  Pandalus  an?iidlcor>ns,  Eupagurus  Kroyerl^  Unciola 
in-orata^  and  Urticina  crassicornis,  all  brightly  -  colored  species, 
seemed  to  have  lost  none  of  their  intensity  at  the  depth  of  430 
fathoms. 

Besides  the  investigation  of  the  fauna  of  the  bottom  by  means  of 
the  dredge,  every  opportunity  Avas  employed  for  collecting  those 
animals  which  live  in  })art  or  wholly  at  the  surface  of  the  water. 
Notwithstanding  the  unfavorable  character  of  the  weather  during 
most  of  the  time  we  were  at  sea,  towing  nets  were  used,  whenever 
soundings  were  being  made,  and  usually  with  very  good  results. 
Nets  of  small  size  were  several  times  successfully  used  even  Avhen  the 

Trans.  Conn.  Acad.,  Vol.  III.  4  August,  1874. 


26  Smith  and  Harger — St.  George's  Banks  Dredglngs. 

steamer  was  under  weigh.  In  this  way  a  great  number  of  surface 
species  were  collected,  and  a  large  proportion  of  them  are  additions 
to  the  fauna  of  our  coast.  Many  of  these  species  belong  to  genera 
previously  known  only  from  much  farther  south,  or  from  the  eastern 
or  southern  Atlantic,  while  quite  a  number  are  undescribed. 

August  29,  on  and  near  Cultivator  Shoal  {k),  where  the  surface 
temperature  of  the  water  was  62°,  the  following  were  taken  :  Trachy- 
nema  digitale  A.  Agassiz,  Pleurobrachia  rhododactyla  Agassiz,  species 
of  Sagitta  and  Aidolytus,  several  species  of  Copeopod  Crustacea, 
Calliopius  Icevhisculus  Boeck  (among  floating  rock-weed),  the  young 
of  some  Brachyuran  in  the  zoea  and  megalops  stages  of  growth,  and 
a  species  of  31otella  (?). 

East  of  George's  Bank,  in  latitude  41°  20'  to  30',  longitude  63° 
to  63°  30',  September  14,  during  the  day,  many  species  were  taken, 
but  as  they  all  occurred,  with  many  additional  species,  on  the  follow- 
ing day,  it  is  not  necessary  to  enumerate  them  separately. 

On  the  evening  of  September  14,  from  nine  to  ten  o'clock,  still  east 
of  the  Bank  (m),  in  latitude  41°  25',  longitude  63°  55',  while  the  sur- 
face temperature  was  65°,  the  following  forms  occurred :  Pleuro- 
hrachia  sp. ;  a  species  of  Salpa  in  abundance  ;  several  species  of 
Heteroi^ods  and  Pteropods,  among  the  latter  Sjnrialis  Gouldii 
Stimpson,  and  species  of  Styliola  j  a  species  of  Sagitta,'  a  species  of 
Sapphiri^ia  and  a  great  many  other  Copeopods ;  species  of  Syj^eria, 
Phrosina^  and  of  another  allied  genus ;  a  species  of  Thysa)iopoda, 
which  was  beautifully  phosphorescent ;  young  Brachyura  in  the  zoea 
and  megalops  stages,  and  the  young  of  some  Macrouran. 

September  15,  on  the  same  line  of  soundings,  in  latitude  41°  25', 
longitude  65°  5'  to  30',  the  temj^erature  of  the  water  varying  from  66° 
to  V0°,  but  most  of  the  time  at  the  latter  point,  very  many  species 
occurred,  and  among  them  the  following:  Physalia pelagica  Lamarck 
(Portuguese  man-of-war),  Cestum  Veneris  Lesueur  (?),  Stomolophus 
meleagris  Agassiz,  Charyhdea  periphylla  Peron  and  Lesueur,  Pelagia 
cyanella  Peron  and  Lesueur ;  species  of  Salpa  and  Sagitta  in  great 
abundance  ;  Lepas  pectinata  Spengler  and  L.  fascicularis  Ellis  and 
Solander ;  two  species  of  Sapphirina  and  many  other  genera  of  Coj^e- 
opoda ;  species  of  Oxycephalus,  Platyscelus,  Pronoe^  Anchyloinera^ 
ThyropuSy  Phronima  (?),  and  Hyperia;  Calliopius  Imviiiscidus  Boeck, 
common  among  floating  rock-weed  ;  species  of  Lucifer  and  Mysis  ; 
Latreiites  ensiferus  Stimpson,  JVautdognq)sus  mimdus  Edwards,  and 
Neptunus  Sayi  Stimpson  among  gulf-weed,  and  the  latter  frequently 
seen  swimming  at  some  distance  from  the  sea-weed  ;  three  species  of 
Heteropods  and   ten   species   of  Pteropods,   all   new  to   our   coast. 


Smith  and  Harger — St.  George's  Banks  Dredgings.  27 

Among  the  Pteropods  are  Styliola  acus  (Eschscholtz  sp.),  and  four 
other  species  of  the  same  genus,  two  of  Pleuropus,  Spirialis  Gouldii, 
etc.  Many  of  these  species  and  genera  are  quite  new  to  the  fauna  of 
the  United  States,  and  nearly  all  of  them  to  the  coast  of  New 
England.  They  are  nearly  all,  as  far  as  known,  characteristic  Gulf 
Stream  forms. 

Notes  on  some  of  the  Species  enumerated ;  by  S.  I.  Smith.* 
Crustacea. 
Eupagurus  Bernhardus  Brandt. 

Pagurus  Bernhardus  (Linne  sp.)  Fabricius,  Entomologia  systematica,  ii,  p.  469,  1793, 

and  Supplementum,  p.  411,  1798. 
Pagurus  (subgenus  Eupagurus,  section  SirejJtodactylus)  Bernhardus  Brandt,  Midden- 

dorff's  Sibirische  Reise,  Krebse,  p.  106,  1851. 
Eupagurus  Bernhardus  Stimpson,  Crust.  Pacific  Shores  of  North  America,  Journal 

Boston  Soc.  Nat.  Hist.,  vi,  p.  483  (separate  copies,  p.  43),  1857. 

1  have  recently  f  wrongly  given  Stimpson  as  authority  for  this  and 
the  next  species,  not  having  at  the  time  access  to  Brandt's  work,  and 
not  being  able  to  comprehend  his  absurdly  complex  nomenclature 
from  the  quotation  of  his  names  by  other  authors. 

Eupagurus  pubescens  Brandt. 

Pagurus  p>ubescei-ts  Kroyer  (in  part),  Gronlands  Amfipoder,  p.  68,  1838,  and  Natur- 

historisk  Tidsskrift,  ii,  p.  251,  1839. 
Pagurus  (subgenus  Eupagurus,  section    Orthodactylus)  pubescens  Brandt,  op.  cit.,  p. 

Ill,  1851. 
Eupagurus  pubescens  Stimpson,  Prodromus  descriptionis  Animalium  evertebratorum, 

etc..   Proceedings  Acad.  Nat.   Sci.,  Pliiladelphia,  1858,  p.  237  (separate  copies,  p. 

75),   1859,  and  Notes  on  North  American  Crustacea,  Annals  Lyceum  Nat.  Hist., 

New  York,  vii,  p.  89  (separate  copies,  p.  43),  1859. 

This  species  is  common  on  our  eastern  coast  north  of  Cape  Cod, 
but  is  not  quite  as  abundant  as  the  last  species  and  is  seldom  found 
at  low  water.  South  of  Cape  Cod  it  is  apparently  confined  to  the 
deeper  and  colder  waters. 

*With  the  exception  of  the  portion  relating  to  the  Crustacea,  these  notes  have  had 
the  benefit  of  Professor  Verrill's  revision,  and  the  descriptions  of  all  the  new  species 
have  been  copied  from  his  pubhshed  papers,  or,  in  the  case  of  those  here  for  the  first 
time  described,  have  been  prepared  by  him  specially  for  these  pages,  and  are  marked 
by  his  initials. 

\  Report  upon  the  Invertebrate  Animals  of  Vineyard  Sound,  in  Report  of  the  U.  S. 
Commissioner  of  Fish  and  Fisheries,  Part  I,  1873  (published  in  1874). 


28  Smith  and  Harger — St.  George's  Banks  Dredgings. 

Eupagurus  Kroyeri  Stimpson. 

Notes  on  North  American  Crustacea,    Annals  Lyceum  Nat.   Hist.,  vii,  p.  89  (43)' 
1859. 

This  species  is  A^ery  closely  allied  to  the  last  and  is  very  easily  con- 
founded with  it,  especially  when  young.  The  diflerences  in  the  rela- 
tive proportions  of  the  chelipeds  and  ambulatory  legs,  given  by 
Stimpson,  will  not  hold  for  distinguishing  the  two  species,  but  the 
diiferences  in  the  amount  of  pubescence  and  especially  in  the  form 
and  armature  of  the  chelipeds  seem  to  be  constant  characters,  suffi- 
cient for  distinguishing  them. 

The  Kroyeri  has  about  the  same  range,  on  our  coast,  as  the  last 
species,  although  I  have  never  seen  it  south  of  Cape  Cod,  but  is 
apparently  less  abundant  and  more  confined  to  the  deeper  waters. 

Sabinea  septemcarinata  Owen  (Sabine  sp.) 

This  species  was  dredged  in  68  fathoms  off  Casco  Bay  in  the  sum- 
mer of  1878.  It  has  also  been  found  by  Mr.  Whiteaves  in  the  Gulf 
of  St.  Lawrence  and  by  Dr.  Packard  on  the  coast  of  Labrador.  It  is 
an  exceedingly  arctic  and  circumpolar  species. 

Caridon  Gordoni  Goes  (Bate  sp.  ?) 

Goes,  Crustacea  decapoda  podophthalma  marina  Suecipe  (from  (Efversight  af  Kongl. 
Vetenskaps-Akad.  Forliandlingar,  Stockholm,  IHtiS),  p.  10. 

We  have  dredged  this  species  in  50  fathoms  in  the  Bay  of  Fundy, 
and  Dr.  Packard  and  Mr.  Cooke  obtained  it  on  Cashe's  Ledge  in  1873. 

Our  specimens  agree  well  with  the  detailed  description  given  by  Goes, 
except  that  they  have  a  well  developed  epipodus  ("  flagellum")  upon 
the  second,  third  and  fourth  cephalothoracic  legs,  as  in  some  species  of 
Hippolyte^  while  Goes  says  of  the  second  legs,  "  nee  palpo  nee  (quoad 
viderim)  flagello  ullo  instructis,"  and  of  the  third  to  fifth,  "  flagellum 
basale  nullum  inspicere  potui."  From  the  guarded  manner  in  which 
Goes  mentions  these  wholly  negative  characters,  I  am  inclined  to  re- 
gard them  as  doubtful.  Our  specimens  agree  so  completely  in  all 
other  respects  that  it  seems  highly  improbable  that  they  should  be 
distinct  from  the  European  species. 

Diastylis  quadrispinosa  G.  0.  Sars. 

(Efversight  af  Kongl.  Vetenskaps-Akademiens  Forhandlingar,  1871,  Stockholm,  p. 
27  ;  and  Beskrivelse  af  de  Paa  Fregatten  Josephiens  Expedition  Fundne  Cumaeeer, 
in  Kongl.  Svenska  Vetenskaps-Akademiens  Handliugar,  ix,  p.  28,  plates  10,  11, 
figs.  51-61,  1871. 

This  is  the  most  abundant  species  of  the  genus  from  off  Buzzard's 
Bay  and  Vineyard  Sound  to  Nova  Scotia.  It  ranges  north  at  least 
as  far  as  the  Gulf  of  St.  Lawrence. 


Smith  and  Harger — St.  George's  Banks  Dredgings.  29 

Diastylis  sculpta  G-  0.  Sars. 

Loc.  cit.,  CEfversight,  p.  71  ;  Handlingar,  p.  24,  pis.  1-9,  figs.  1-49. 
This  species  is  not  uncommon  in  Casco  Bay  and  the  Bay  of  Fundy. 
Phoxus  Kroyeri  Stimpson. 

Marine  Invertebrates  of  Grand  Manan,  p.  58,  1853. 

We  have  dredged  this  species  in  10  to  29  fathoms  in  and  off  Viue- 
yai'd  Sound,  on  sandy  and  muddy  bottoms  in  shallow  water  in  Casco 
Bay,  and  have  found  it  from  low  water  to  20  fathoms  in  the  Bay  of 
Fundy.  Mr.  Whiteaves  has  dredged  it  in  the  Gulf  of  St.  Lawrence 
in  200  fathoms,  muddy  bottom. 

Our  species  is  very  closely  allied  to,  and  probably  identical  with, 
the  P.  Holbollii  Kroyer  which  is  found  in  Greenland,  Iceland  and 
northern  Scandinavia. 

Harpina  fusiformis  Smith. 

Phoxus  fusiformis  Stimpson,  Marine  Invertebrates  of  Grand  Manan,  p.  57,  1853. 

This  species  is  very  likely  identical  with  the  II.  plwiiosa  Boeck 
{Phoxus  plumosus  Kroyer),  which  has  very  nearly  the  same  range  as 
Phoxus  Holhollii. 

We  have  dredged  our  species  in  20  to  60  fathoms,  muddy  bottom, 
in  the  Bay  of  Fundy.  Mr.  Whiteaves  has  dredged  it  frequently,  in 
the  Gulf  of  St,  Lawrence. 

Stenothoe  peltata  Smith,  sp.  nov. 

Plate  IV,  figures  5  to  8. 
Female.  Eyes  round  and  nearly  white  in  alcoholic  specimens. 
Antennuloe  considerably  shorter  than  the  epimera  of  the  fourth  seg- 
ment; first  segment  of  the  peduncle  stout,  fully  as  long  as  the  head, 
the  second  shorter,  and  the  third  very  short  and  like  the  segments  of 
the  flagellum ;  flagellum  scarcely  longer  than  the  peduncle,  com- 
posed of  about  eight  segments.  Antennje  slightly  longer  than  the 
antennula?;  the  ultimate  and  penultimate  segments  of  the  peduncle 
about  equal  in  length;  flagellum  about  as  long  as  the  flagellum  of  the 
antennulae.  Second  epimeron  (figure  5)  rudely  ovate,  twice  as  high  as 
broad ;  third  somewhat  rectangular,  no  wider  than  the  second  but 
considerably  deeper ;  foiirth  (figure  6)  very  large,  slightly  deeper  than 
the  third  and  a  third  or  a  fourth  longer  than  deep,  being  about  as  long 
as  the  first  five  segments  of  the  thorax,  the  inferior  margin  regularly 
curved  and  the  posterior  convex  in  outline.  First  legs  (figure  7) 
small  and  slender;  merus  triangular  and  broader  distally  than  the 
carpus,  which  is  not  quite  twice  as  long  as  broad  and  has  the  lateral 
margins  parallel ;  propodus  narrower  but  slightly  longer  than  the 
carpus  and  narrowed  distally  ;  dactylus  about  half  as  long  as  the  jjro- 


30  Smith  and  Harger — St.  George's  Banks  Dredgings. 

podus.  Second  legs  (figure  5)  stouter;  merus  short  triangular; 
carpus  much  broader  than  long  and  only  slightly  produced  beneath 
the  propodus;  propodus  about  as  long  as  the  breadth  of  the  epinieron, 
nearly  twice  as  long  as  broad ;  palmary  margin  (figure  8)  convex  in 
outline,  slightly  oblique,  with  an  acute  lobe  and  a  spine  at  the  pos- 
terior angle,  within  which  the  tip  of  the  dactylus  closes.  Third  and 
fourth  legs  slender  and  nearly  naked.  Basal  segment  in  the  fifth  legs 
slender,  foitr  times  as  long  as  broad,  not  wider  than  the  merus.  Sixth 
and  seventh  legs  slightly  shorter  than  the  fifth,  the  basal  segments 
posteriorly  dilated  and  squamiform  in  both  pairs,  but  broader  in  the 
seventh  than  in  the  sixth.  Posterior  caudal  stylets  with  the  ramus 
slightly  longer  than  the  peduncle. 

Length  of  largest  specimen,  from  front  of  head  to  tip  of  telson, 
about  6™"'. 

The  mandibles  are  without  palpi  or  molar  tubercles,  and  in  all 
other  characters  the  species  agrees  with  the  genus  Stenothoe  as 
restricted  by  Boeck,  but  it  seems  to  be  very  distinct  from  either  of 
the  European  species. 

Near  Cultivator  Shoal  (haul  Z*),  30  fathoms,  soft,  sandy  bottom, 
August  29. 

Syrrhoe  crenulata  Goes. 

Crustacea  amphipoda  maris  Spetsbergiam  alluentis,  CEfversight  af  Kongl.  Vetens- 
kaps-Akad.   Forhandlingar,  Stockholm,  1865,  p.  527.  pi.  xl,  fig.  25;  Boeck,  Crus- 
tacea amphipoda  borealia  et  arctica  (Vidensk.-Selskabs  Forhandlinger,  Christiania, 
1870),  p.  67,  1870. 
We  have  also  dredged  this  species,  in  1872,  in  12  fathoms  in  John- 
son's Bay,  near  Eastport,  Maine,  and  in  90  to  100  fathoms  off  Grand 
Menan,  and  have  examined  specimens  dredged,  in  1873,  in  30  fath- 
oms, in  Gaspe  Bay,  Gulf  of  St.   Lawrence.     Our  specimens  have  all 
been  considerably  larger  than  the  one  figured  by  Goes,  but  otherwise 
agree   perfectly.     It  seems  to  be  an  exceedingly  arctic  form,  being 
found  in  Europe  from  Spitzbergen  to  the  western  coast  of  Norway. 

Tiron  acanthurus  Liiijeborg. 

Boeck,  op.  cit.,  p.  69.  Syrrhoe  hicmpis  Goes,  loc.  cit.,  p.  528,  pi.  xl,  fig.  26.  f  Thes- 
sarops  hastata  Norman,  Annals  and  Magazine  Nat.  Hist.,  IV,  ii,  p.  412,  pi.  xxii,  figs. 
4-7,  1868. 

This  species  has  apparently  not  been  noticed  on  our  coast  before. 
It  has  been  found  in  Greenland,  Finmark,  and  on  the  western  coast 
of  Norway,  while  Norman's   TJcessarops  was  from  the  English  coast. 

CEdiceros  lynceus  Sars. 

Oversigt  over  nordsk-arct.  Krebsdyr.  Forhandl.  i  Vidensk-Selsk.  i  Christiania,  1858, 
p.   143  (teste  Boeck);  Boeck,  op.  cit.,  p.  82.     CEdiceros propinquus  Goes,  loc.  cit.. 


Smith  and  Harger — 8t.  George's  Banks  Bredgings.  31 

p.  526,  1865,  pi.  xxxix,  fig.  19.     Monoculodes  nuhilius  Packard,  Memoirs  Boston 
See.  Nat.  Hist,  i,  p.  398,  1867. 

We  dredged  this  species  in  the  Bay  of  Fundy  in  1868  and  18Y2, 
the  latter  year  in  60  to  80  fathoms  ;  in  Casco  Bay,  in  27  ftithonis,  in 
1873,  and  Dr.  Packard  and  Mr.  C-ooke  obtained  it  at  several  local- 
ities, in  the  "  Gulf  of  Maine,"  from  50  to  90  fathoms,  on  the  expedi- 
tion of  the  Bache  in  1873.  I  have  also  examined  specimens  dredged 
in  the  Gulf  of  St.  Lawrence  by  Mr.  Whiteaves  and  on  the  coast  of 
Labrador  by  Dr.  Packard.  It  extends  to  Greenland,  Iceland,  Spitz- 
bergen  and  Finmark. 

Monoculodes  borealis  Boeek. 

Op.  cit,  p.  88,  1870.  (Ediceros  affinis  Goes,  loc.  cit.,  p.  527,  pi.  xxxix,  fig.  21',  1865 
(non  Bruzelius). 

This  species  is  recorded  from  Spitzbergen  and  northern  Norway 
by  Goes  and  Boeck,  but  seems  not  to  have  been  noticed  on  this  side 
of  the  Atlantic  before. 

Paramphithoe  pulchella  Bruzelius  (Kroyer  sp.) 

We  have  dredged  this  species  off  Casco  Bay  and  in  the  Bay  of 
Fundy,  on  hard  bottoms,  in  from  40  to  90  fathoms,  and  it  was 
dredged  on  Cashe's  Ledge  and  Stellwagen's  Bank,  in  1873,  by  Dr. 
Packard  and  Mr.  Cooke.  It  extends  north  to  the  Gulf  of  St.  Law- 
rence, and,  according  to  Boeck,  to  Greenland,  Iceland,  Spitzbergen, 
and  the  western  coast  of  Norway. 

Paramphithoe  cataphracta  Smith. 

AmpMthonotus  cataphi-adus  Stimpson,  Synopsis  of  the  Marine  Invertebrata  of  Grand 
Manan,  p.  52,  185.'i  (description  copied  in  Bate,  Catalogue  of  Amphipodus  Crus- 
tacea in  the  British  Museum,  p.  152,  1862.) 

This  species  is  apparently  a  true  Paramphithoe,  as  restricted  by 
Boeck,  and  closely  allied  to,  if  not  identical  Avith,  P.  pano2)la  Bru- 
zelius [Aynphithoe  pjaaopla  Kroyer).  Boeck  places  Pleustes  tiibercii- 
latus  Bate  as  a  synonym  of  Kroyer's  species,  and  if  he  is  correct  in 
this,  our  species  is  undoubtedly  distinct.  The  cataphracta  appears  to 
be  an  inhabitant  of  hard  or  coarse  sandy  and  shelly  bottoms  from  5 
to  50  fathoms.  We  have  dredged  it  sparingly  in  Casco  Bay  and  the 
Bay  of  Fundy,  and  Dr.  Packard  has  dredged  it  on  the  coast  of 
Labrador. 

VertUmnuS  serratUS  ?  Goes  (Fabricius  sp.) 

Acanfhonotm  serratus  Stimpson,  Synopsis  of  the  Marine  Invertebrata  of  Grand 
Manan,  p.  52,  1853. 

Our  specimens  all  differ  from  the  descriptions  and  figures  given  by 
Boeck  and  Kroyer  in  the  armature  of  the  posterior  margin  of  the 


32  Smith  and  Harger — St.  G-eorge's  Banks  Dredgings. 

thii'd  segment  of  the  abdomen.  In  our  specimens  the  upper  process 
from  this  margin  is  armed  with  four  or  five  teeth  above  and  at  the 
tip,  while  the  lower  process  is  armed  with  five  or  six  teeth  similarly 
situated,  but  with  no  teeth  on  the  lower  margin  except  just  at  the 
tip.  In  Kroyer's  figure  (Gronlands  Ampfipoder,  plate  ii,  figure  8) 
the  upper  process  is  represented  as  terminating  in  a  single  tooth  and 
the  lower  process  as  toothed  along  both  sides ;  Boeck's  description 
agrees  with  this  except  that  he  says  there  are  two  teeth  at  the  tip  of 
the  upper  process. 

It  is  not  uncommon  on  hard  bottoms  in  from  5  to  50  fathoms  in 
the  Bay  of  Fundy.  We  have  also  dredged  it  in  Casco  Bay  and  have 
received  it  from  the  Gulf  of  St.  Lawrence,  where  it  was  dredged  by 
Mr.  Whiteaves. 

Acanthozone  cuspidata  Boeck. 

This  species  is  quite  common  on  hard,  and  especially  on  spongy 
bottoms  in  5  to  40  fathoms  in  the  Bay  of  Fundy,  although  it  is  not 
mentioned  by  Stimpson  in  his  work  on  Grand  Menan.  We  have  also 
dredged  it  in  Casco  Bay,  and  Mr.  Whiteaves  has  obtained  it  in  the 
Gulf  of  St.  Lawrence.  It  ranges  to  Greenland,  Spitzbergen  and 
Finmark. 

BybliS  Gaimardi  Boeck  (Kroyer  Bp.) 

We  have  frequently  dredged  this  species  in  Casco  Bay  and  the 
Bay  of  Fundy,  on  muddy  bottoms  in  10  to  60  fathoms.  It  extends 
north  to  the  Gulf  of  St.  Lawrence  (Whiteaves),  Labrador  (Packard), 
and,  according  to  Boeck,  to  Greenland,  Iceland,  Spitzbergen  and 
Norway.  The  Ampelisca  Gahnardi  of  Bate,  and  Bate  and  West- 
wood,  is  not  this  species  but  a  true  Ampelisca. 

All  the  species  of  this  sub-family  are  undoubtedly  tube  dwellers. 
Lilljeborg  noticed  the  habit  in  HaploOps  ;  it  has  been  observed  in 
species  of  Ampelisca  by  Professor  Verrill  and  myself.  In  this 
species,  the  glands  which  secrete  the  cementing  fluid  are  situated 
principally  in  the  meral  and  basal  segments  of  the  third  and  fourth 
pairs  of  thoracic  legs. 
Xenoclea  megachir  Smith,  sp.  nov. 

Plate  IV,  figures  1  to  4. 

Male.  Eyes  large,  black,  very  slightly  elongated,  and  approaching 
closely  the  edges  of  the  triangular  prominence  of  the  inferior  angle 
of  the  front  margin  of  the  head.  Peduncle  of  the  anteninila'  about 
as  long  as  the  head  and  the  first  two  segments  of  the  thorax,  the 
second  segment  longest,  the  first  and  third  about  equal  in  length, 


Smith  and  Sarger — St.  George's  BanJcs  Dredgings.  33 

flagellum  about  as  long  as  the  peduncle  and  composed  of  twelve  to 
sixteen  segments.  Antennae  a  little  longer  than  the  antennulae ; 
ultimate  and  penultimate  segments  of  the  peduncle  sub-equal  in 
length ;  flagellum  slightly  shorter  than  the  peduncle  and  composed 
of  eleven  to  fifteen  segments.  First  epimeron  (figure  1)  as  broad  as 
high ;  second  (figiu-e  2)  broader  than  high ;  third  (figure  3)  and 
fourth  not  broader  than  high  and  successively  deeper  than  the  first 
and  second  ;  fifth  (figure  4)  slightly  deeper  than  the  fourth  and  its 
terminal  portion  as  broad.  In  the  first  legs  (figure  1),  the  carpus 
longer  and  broader  than  the  propodus,  which  is  somewhat  oval  and 
twice  as  long  as  broad  ;  the  dactylus  slender,  slightly  curved  and 
fully  as  long  as  the  propodus.  The  inferior  distal  margin  of  the  pro- 
podus is  regularly  curved  to  a  short  distance  from  the  extremity, 
where  there  is  a  small  but  deep  emargination,  beyond  which  and 
round  upon  the  short  distal  margin  the  edge  is  serrate  with  minutely 
crenulated  teeth  ;  the  posterior  margin  is  furnished  with  numerous 
slender  seta?  and  with  a  single  stout  spine  at  the  emargination  near 
the  distal  end.  The  inner  edge  of  the  dactylus  is  armed  with  a  series 
of  acute  teeth  directed  obliquely  toward  the  tip.  In  the  second  pair 
of  legs  (figure  2)  the  propodus  is  very  stout,  about  twice  as  long  as 
the  epimeron  and  scarcely  one-half  longer  than  broad ;  the  palmary 
margin  oblique  and  armed  near  the  middle  with  two  stout  obtuse 
teeth  ;  the  dactylus  stout  and  its  inner  edge  sinuous.  Third  (figure 
3)  and  fourth  pair  of  legs  alike ;  ischium  and  carpus  short,  each 
nearly  or  quite  as  broad  as  long;  merus  fully  as  long  as  the  epimeron 
and  half  as  broad  as  long ;  propodus  slender,  not  more  than  half  as 
broad  as  the  carpus  but  twice  as  long  ;  dactylus  slender,  about  half 
as  long  as  the  propodus.  Basal  segment  in  the  fifth  legs  (figure  4) 
squamiform,  oval,  nearly  as  broad  as  long  and  with  a  mai-ked  angular 
emargination  at  the  inferior  posterior  angle ;  carpus  only  slightly 
longer  than  the  breadth  of  the  raerus  ;  dactylus  slightly  curved  and 
acute.  Second  and  third  segments  of  the  abdomen  with  the  inferior 
portion  of  the  posterior  margin  sinuous,  and  the  inferior  angle 
prominent,  but  scarcely  less  than  right-angled.  The  outer  rami  in 
all  the  caudal  stylets  slightly  shorter  than  the  inner,  and  all  the  rami 
armed  with  short  spines  above  and  more  slender  spines  at  the  tips. 
Telson  stout,  about  as  broad  as  long  and  scarcely  more  than  half  as 
long  as  the  peduncle  of  the  posterior  caudal  stylets,  the  posterior 
margin  with  a  few  setiform  hairs  each  side. 

In  the  female  the  hands  in  the  second  pair  of  limbs  are  propor- 
tionally much  smaller  and  more  abundantly  provided  with  hairs, 
while  the  teeth,  or  lobes  of  tha  palmary  margin,  are  further  apart  and 

Teans.  Conn.  Acad.,  Yol.  III.  5  August,  1874. 


34  Smith  and  Harget — St.  George's  Banks  Dredgings. 

separated  by  a  broad  and  deep,  rounded  sinus  ;  the  dactyhis  is  not 
so  stout,  and  has  the  inner  margin  evenly  curved  and  serrated. 

Length,  from  front  of  head  to  tip  of  telson,  5  5  to  Y'o""'. 

I  refer  this  species  with  some  hesitation  to  Boeck's  genus  Xenoclea, 
which  is  known  to  me  only  from  the  very  short  diagnosis  of  the  genus 
and  of  the  single  species  X.  Batei,  given  in  his  Crustacea  Amphipoda 
Borealia  et  Arctica,  p.  155.  "  Pedes  3tii  et  4ti  paris  articulo  Imo 
latissimo"  of  the  generic  diagnosis  would  scarcely  apply  to  our 
species,  but  in  all  the  other  generic  characters  it  agrees  perfectly,  as 
it  does  also  with  the  diagnosis  of  the  sub-family  Photinoe,  except 
that  the  mandibles  each  bear  six  serrated  spines  instead  of  the  usual 
numbei-,  four. 

Near  Cultivator  Shoal  (haul  J),  30  fathoms,  soft,  sandy  bottom, 
August  29  ;  and  on  the  northern  side  of  George's  Bank  (haul  q), 
north  latitude  42°,  west  longitude  67°  42',  45  fathoms,  coarse  sandy 
bottom.     Also,  in  18  fathoms,  off  Watch  Hill,  Rhode  Island. 

When  first  examining  the  alcoholic  specimens  of  this  species,  I 
noticed  a  peculiar  opaque  glandular  structure  filling  a  large  portion 
of  the  third  and  fourth  pairs  of  thoracic  legs,  which  in  most,  if  not 
all,  the  non-tul)e-building  Amjihipoda  are  wholly  occui)ied  by  muscles. 
A  further  examination  shows  that  the  terminal  segment  (dactylus)  in 
these  legs  is  not  acute  and  claw-like,  biit  truncated  at  the  tip  and 
apparently  tubular.  In  this  sjiecies,  a  large  cylindrical  portion  of 
the  gland  lies  along  each  side  of  the  long  basal  segment,  and  these 
two  portions  uniting  at  the  distal  end  pass  through  tlie  ischial  and 
along  the  jiosterior  side  of  the  meral  and  carpal  segments  and  doubt- 
less connect  with  the  tubular  dactylus.  (See  Plate  III,  figure  3.) 
There  can  be  no  doubt  that  these  are  the  glands  which  secrete  the 
cement  with  which  the  tubes  are  built,  and  that  these  two  pairs  of 
legs  are  specialized  for  that  purpose.  A  hasty  examination  revealed 
a  similar  structiu'e  of  the  corresponding  legs  in  Ainjy/iithoe  macidata, 
Ptilocheirus  pinguis,  Cerapus  rubricomis,  Byblis  Gaimardi,  and  a 
species  of  Ampelisca.  In  all  these  except  the  last  two  a  very  large 
proportion  of  the  gland  is  in  the  basal  segment.  In  the  Amphithoe 
this  segment  is  thickened  and  the  gland  is  in  the  middle.  In  the 
Cerapus  it  is  very  broad  and  almost  entirely  filled  by  the  gland,  with 
only  very  slender  muscles  through  the  middle,  and  the  orifice  in  the 
dactylus  is  not  at  the  very  tip  but  sub-terminal  on  the  posterior  side. 
In  the  Ptilocheirus  the  gland  forms  three  longitudinal  masses  in  the 
basal  segment  and  is  also  largely  developed  in  the  meral  and  carpal 
segments.  The  dactylus  is  long  and  slender  and  the  orifice  sub-ter- 
minal. In  Ampelisca  and  Byhlis  (which,  like  Saploops,  are  tube- 
building  genera)  the  meral  segments  of  the  specialized  legs  are  nearly 


Smith  and  Harcjer — St.  George's  Banks  Dredgings.  35 

as  large  as  the  basal  and  contain  a  proportionally  large  part  of  the 
gland. 

ScapellTim  Stroemi  Sars. 

Plate  in,  fignre  9. 

I  am  not  aware  that  a  description  of  this  species  has  yet  been  pub- 
lished, although  the  name  was  used  by  Prof.  Michael  Sars  in  his  list 
of  animals  living  at  great  depths  in  the  sea,  published  in  1869,*  and 
the  species  has  since  been  incidentally  figured,  without  any  detail, 
on  the  stems  of  Mopsea  borealis,  by  Dr.  G.  O.  Sars  in  his  recent  work 
on  "  Some  Remarkable  Forms  of  Animal  Life  from  Great  Depths  off" 
the  Norwegian  Coast"  (Plate  V,  figure  2).  Dr.  G.  O,  Sars  has,  how- 
ever, very  kindly  compared  a  drawing  of  one  of  our  specimens,  and 
he  writes  me  that  it  agrees  in  every  detail  Avith  the  Norwegian  form. 
It  is  very  distinct  from  any  of  the  species  described  in  Darwin's  great 
work,  and  also  from  the  species  recently  described  from  the  Challenger 
Expedition. 

Since  our  specimens  were  obtained  from  430  fathoms.  Dr.  Packard 
and  Mr.  Cooke  have  dredged  in  50  to  70  fathoms  near  Cashe's  Ledge, 
and  in  142  fathoms,  20  miles  east  of  Cape  Race  (both  localities  within 
the  "  Gulf  of  Maine").  AH  the  specimens  were  attached  to  stems  of 
hydroids.  On  the  Norwegian  coast  the  species  has  the  same  habit 
and  has  been  found  by  Dr.  G.  O.  Sars  in  from  80  to  300  fathoms. 

Annelida. 
Lsenilla  (?)  mollis  6.  0.  Sars. 

Bidrag  til  Kundskaben  om  Christianiafjordens  Fauna,  iii,  p.  7,  plate  xiv,  figs.  1-12, 
1873. 

Body  large,  rather  stout,  medially  convex.  Head  short  and 
broad,  narrowed  posteriorly,  prominently  rounded  laterally,  and  pro- 
duced into  two  very  small  conical  points  anteriorly.  The  anterior 
eyes  are  larger  than  the  others,  situated  on  the  outer  and  upper  sur- 
face of  the  lateral  prominences,  and  look  outward  and  upward  ;  the 
posterior  pair  are  nearer  together,  on  the  lateral  slopes  of  the  nar- 
rowed part  of  the  head.  The  median  tentacle  is  wanting  in  our  speci- 
men, but  its  basal  segment  is  of  moderate  size  and  cylindro-conical ; 
the  antennje  are  slender,  and  nearly  three  times  the  length  of  the 
head,  banded  with  brown  ;  the  palpi  are  rather  slender  and  regularly 
tapered,  smooth,  or  nearly  so,  four  or  five  times  the  length  of  the 
head.  The  dorsal  and  tentacular  cirri  and  the  scales  are  wanting  in 
the  single  specimen  obtained.     The  lateral  appendages  are  large  and 

*  Forhandlinger  i  Videnskabs-Selskabet  i  Christiania,  1868,  p.  259,  1869. 


36  Smith  and  Harger — St.  George's  J^cmJcs  Dredgings. 

prominent,  with  large  fascicles  of  long,  slender  seta?  in  the  lower  rami, 
and  much  shorter  and  stouter  ones  in  the  upper  rami.  The  appenda- 
ges, including  setae,  equal  or  exceed  the  breadth  of  the  body.  Breadth 
of  body,  exclusive  of  appendages,  7™™  ;  length  of  the  latter,  without 
setaa,  S-S"^""  ;  with  setaj,  10'"";  length  of  body  to  the  15th  segment, 
25™"\  The  setae  of  the  upper  ramus  are  very  stout,  and  all  of  nearly 
the  same  form,  the  upper  ones  being  merely  smaller  and  stouter  than 
the  rest ;  they  are  nearly  straight  or  slightly  recurved,  with  rather 
conspicuous,  moderately  close  transverse  series  of  denticles,  which  ex- 
tend nearly  to  the  ends,  leaving  only  stout,  naked,  straight  tips.  The 
setae  of  the  lower  ramus  are  much  longer  and  far  more  slender,  with 
a  long,  slender  shaft,  and  a  slightly  expanded  terminal  portion,  which 
is  conspicuously,  but  not  closely,  spiniilated  on  both  sides  to  the  tips ; 
many  of  these  are  nearly  straight,  but  most  are  slightly  curved ;  the 
upper  ones  are  most  slender,  and  mostly  have  the  tips  only  very 
slightly  bidentate,  and  the  spinules  exceed  the  diameter  of  the  setae 
and  increase  toward  the  end,  the  last  ones  projecting  considerably 
beyond  the  tip  ;  the  middle  ones  are  about  twice  as  stout,  having  the 
terminal  part  more  expanded ;  their  spinulation  is  similar,  but  the 
tips  are  more  distinctly,  though  slightly,  bidentate,  the  denticles  be- 
ing partially  obscured  by  the  terminal  spinules  that  project  beyond 
them ;  the  lower  ones  are  moi-e  slender  and  like  the  upper  ones  in 
form  and  character. 

Near  St.  George's  Bank,  110  fathoms,  mud.  Coast  of  Norway,  40- 
200  fathoms  (G.  O.  Sars). 

Our  specimen  is  imperfect,  but  the  head  and  seta?  are  quite  peculiar. 
The  latter  are  remarkable  for  the  length  of  the  spinules,  and  for  the 
minuteness  of  the  denticles  at  the  tips. — A.  E,  V. 

Antinoe  angusta  Verriii,  sp.  nov. 

Body  narrow,  rather  slender,  elongated,  tapering  gradually  pos- 
teriorly. Head  small,  short,  rounded,  broader  than  long,  the  lateral 
lobes  short,  not  prolonged  into  points  anteriorly,  but  obtusely  rounded ; 
the  lateral  borders  also  well  rounded.  Eyes  small,  nearly  equal ;  the 
postei-ior  pair  situated  on  the  dorsal  side  of  the  vertex ;  the  anterior 
pair  farther  apart  on  the  outer  and  upper  surfoce  of  the  lateral  promi- 
nences. Tentacle  long  and  very  slender,  about  three  times  the  length 
of  the  head;  antennae  small  and  short,  scarcely  one-third  as  long  as 
the  head  ;  palpi  moderately  large,  glabrous,  considerably  longer  than 
the  tentacle.  Dorsal  cirri  slender,  pretty  regularly  but  not  closely 
covered  with  slender  papillae.  The  lateral  appendages,  except  ante- 
riorly, bear  large  fascicles  of  long,  fine  capillary  setae,  which  gives  a 


Smith  and  Harger — 8t.  George's  Banks  Dredgings.  Si 

villous  appearance  to  the  sides.  The  elytra,  in  our  specimen,  are 
wanting.  The  color,  in  alcohol,  is  light  brown,  crossed  by  lighter 
transverse  lines.  Length,  15™'"  ;  breadth,  without  appendages,  2"""  ; 
breadth,  including  setae,  4'"™. 

On  the  middle  segments  the  setae  of  the  upper  ramus  are  quite 
unequal  in  size  and  length ;  the  upper  ones  are  stout,  with  the  ends 
more  or  less  recurved ;  the  middle  ones  are  still  larger  and  more  than 
twice  as  long,  slightly  curved,  and,  like  the  former,  conspicuously 
transversely  serrulate  almost  to  the  extreme  tips ;  the  lower  ones  are 
shorter,  less  stout,  and  slightly  curved.  The  seta3  of  the  lower  ramus 
are  longer  and  extremely  slender;  the  upper  ones  are  mostly  but 
slightly  expanded  in  the  middle,  with  very  long,  flexil)le  capillary 
tips,  finely  tapered  to  the  end,  and  very  minutely  serrulate  or  nearly 
smooth ;  the  median  ones  are  stouter,  more  expanded  in  the  middle, 
with  long,  acuminate,  slender,  sharp  tips,  and  with  conspicuous,  rather 
distant  spinules  on  one  or  both  sides,  which  become  very  fine  and 
moi'e  crowded  distally  ;  tlie  lower  ones  are  much  shorter,  and  have 
shorter  but  still  very  slender  tips,  and  fewer  and  more  distant  spi- 
nules. The  ventral  cirri  are  slender,  tapered,  with  few,  distantly  scat- 
tered, small  papillae. — A.  E.  V. 

Near  Saint  George's  Bank,  150  fathoms,  mud  (locality  s). 

Antinoe  Sarsi  Kinberg. 

Maliagren,  Nordiska  Hafs-Annulater,  (Efversigt  Kongl.  Yetenskaps-Akad.  For- 
handlingar,  Stockholm,  1865,  p.  75,  pi.  9,  fig.  G  ;  Annulata  PolychiBta,  p.  13,  1867. 

Our  specimen  of  this  species  agrees  very  well  with  jMalmgren's 
figures  and  description.  It  is  much  larger  and  stouter  than  the  pre- 
ceding, and  the  head  is  longer  and  quite  different  in  form,  the  lateral 
lobes  extending  forward  into  acute  conical  points. 

The  set£e  are  similar  to  tliose  of  the  former,  but  the  median  and  in- 
ferior setae  of  the  lower  ramus  are  relatively  somewhat  stouter  and  have 
the  tips  less  attenuated  and  elongated,  while  the  spinules  are  larger 
and  more  conspicuous,  especially  on  the  upper  setae  of  the  lower  ramus. 

Near  Saint  George's  Bank,  85  fathoms,  mud.  Gulf  of  Saint  Law- 
rence (Whiteaves,  t.  Mcintosh). — A.  E.  V. 

Encranta  villosa  Maimgren. 

Eucranta  villosa  Maimgren,  Nordiska  Hafs-Annulater,  CEfversigt  af  Kongl.  Vetens- 
kaps-Akad.  Forhandlingar,  Stockholm,  1865,  p.  80,  pi.  10,  fig.  9  ;  Annulata  Poly 
chajta,  p.  1-1,  1867. 

?  Eujiolynoe  occidentalis  Mcintosh,  Annals  and  Magazine  Nat.  Hist.,  IV,  vol.  xiii,  p. 
264,  pi.  9,  figs.  8-13,  1874. 

This  large  species  is  easily  distinguished,  even  when  destitute  of 


38  Smith  and  Harger — St.  George's  JBanks  Dredging s. 

its  scales,  by  the  short,  stout,  strongly  curved  setae  of  the  upper  ra- 
mus, and  much  longer,  slender,  fascicled  settle  of  the  lower  ramus, 
among  which  the  upper  ones  have  a  strongly  spinulose,  slender,  acu- 
minate, terminal  portion,  with  a  nearly  straight,  split,  or  forceps-like, 
slender  tip,  while  the  middle  and  lower  ones  have  a  short,  cuspidate 
terminal  portion,  with  few  large  spinules,  and  naked  acute  tips. 

I  am  unable  to  find  anything  in  the  figures  and  description  of  the 
species  recently  described  by  Mcintosh  to  indicate  that  it  is  distinct 
from  the  present  species,  with  which,  however,  he  has  not  compared  it. 

Near  Saint  George's  Bank,  150  fathoms,  mud  (locality  s).  Gulf  of 
Saint  Lawrence,  110  fathoms  (Whiteaves,  t.  Mcintosh). — A.  E.  V. 

Nephthys  circinata  Verriii,  sp.  nov. 

Body  slender,  elongated,  ratlier  depressed,  tapering  gradually  pos- 
teriorly. Head  sub-pentagonal,  rather  broader  than  long ;  a  pair  of 
short,  tapering  antennae  at  the  anterior  angles,  about  one-fourth  as 
long  as  the  width  of  the  anterior  border  of  the  head  ;  another  pair  of 
longer,  slender,  tapering  antenna;  at  the  lateral  angles ;  tentacular 
cirri  long  and  tapering.  Proboscis  smooth  towai'd  the  base ;  its  dis- 
tal portion  with  rows  of  slender  acute  papillae,  which  increase  rapidly 
in  length  toward  the  end,  where  they  become  very  prominent. 

The  lateral  appendages,  including  the  setae,  are  as  long  as  the 
breadth  of  the  body ;  the  setae  are  very  numerous,  long  and  slender. 
The  caudal  cirrus  is  long  and  slender,  tapering  to  a  slender  tip. 
Length  of  body,  50'"'";  diameter,  2-5'"'"  ;  diameter,  including  append- 
ages, 5'"'". 

The  lateral  appendages  of  the  middle  region  are  moderately  long, 
the  rami  separated  by  a  space  scarcely  equal  to  half  their  height. 
Superior  ramus,  with  a  short,  broad  ovate,  obtuse,  or  slightly  acumi- 
nate upper  lamella,  directed  outward,  and  considerably  exceeding  the 
setigerous  lobe,  and  a  much  smaller  ovate  median  lamella ;  branchial 
cirrus  long,  rather  slender,  tapered,  curved  downward  and  inward  (cir- 
cinate),  forming  rather  more  than  a  complete  whorl ;  the  appendage  at 
its  base,  on  the  anterior  segments,  is  short  and  broad,  subtruncate  dis- 
tally,  and  with  a  small  papilliform  process  projecting  downward  from 
its  lower  angle,  nearly  in  contact  with  the  branchial  cirrus  ;  on  the 
median  segments  it  is  broad  and  long-ovate,  unequally  acuminate, 
leaf-like.  The  lower  ramus  has  a  very  long  and  wide  ligulate  lamella, 
directed  obliquely  upward  and  outward,  usually  more  than  twice  as 
long  as  the  setigerous  lobe,  and  about  equal  to  it  in  width ;  its  lower 
edo-e  at  about  the  middle  is  sometimes  incurved,  and  its  tip  is  acumi- 
nate and   blunt-pointed  ;  the  ventral  cirrus  is  slender  and  tapered. 


Smith  and  Harger — St.  George's  Banks  Dredging s.  39 

The  capillary  seta?  form  large  fascicles  and  are  very  long  and  slender, 
nearly  smooth,  and  with  very  attenuated  tips  ;  their  length  is  about 
three  times  that  of  the  appendages  themselves;  the  transversely 
marked  seta?  are  scarcely  one-fourth  as  long,  and  about  the  same  in 
diameter,  with  very  slender  tips. — A.  E.  V. 

East  of  Saint  George's  Bank,  430  fathoms  (locality  </)  ;  north  of 
Saint  George's  Bank,  85  fathoms,  mud  (locality  jk»). 

Nephthys  ingens  Stimpson. 

SjTiopsis  of  the  Marine  Invertebrata  of  Grand  Manan,  p.  33,  1853;  Verrill,  Report 

on  the  Invertebrate  Animals  of  Vineyard  Sound  and  Adjacent  Waters,  in  Report 

of  U.  S.  Commissioner  of  Fish  and  Fisheries,  part  I,  IS'ZS,  p.  583  (separate  copies, 

p.  289),  plate  xii,  figs.  59,  60,  1874. 
?  Neplithys  incisa  Malmgren,  Q5fversigt  af  Kongl.  Yet.-Akad.  Forhandlingar,  1865,  p. 

105,  plate  xii,  fig.  21. 

This  is  the  most  common  and  abundant  species  on  muddy  bottoms 
in  the  deep  water  along  the  whole  New"  England  coast.  It  occurs  at 
all  depths  from  2  to  430  fathoms. 

It  is  easily  distinguished  by  the  stout  quadrangular  body,  deeply 
incised  posteriorly;  by  the  blackish  setae,  and  by  the  remarkably 
elongated  and  widely  separated  rami  of  the  posterior  appendages. 
There  is  a  long,  odd,  median  papilla  on  the  dorsal  side  of  the  proboscis, 
and  a  smaller  one  beneath  ;  the  papillffi  in  the  longitudinal  rows  are 
rather  small. — A.  E.  V. 

Phyllodoce  catenula  Verrill. 

Report  on  the  Invertebrate  Animals  of  Vineyard  Sound,  in  Report  of  U.  S.  Commis- 
sioner of  Fish  and  Fisheries,  part  I,  1873,  p.  587,  1874 ;  Exploration  of  Casco  Bay 
by  the  U.  S.  Fish  Commission,  Proceedings  American  Association  for  the  Ad- 
vancement of  Science,  1873,  p.  380,  pi.  3,  fig.  1,  1874. 

Plate  IV,  figure  3. 

George's  Bank,  50  fathoms  (locality  d).  It  also  occurs  at  Watch 
Hill,  llhode  Island,  in  4  to  6  fathoms,  among  rocks  and  alga?,  and  in 
tide-pools  ;  at  Wood's  Hole,  at  surface,  evening,  July  3 ;  in  Cuasco 
Bay,  8  to  30  fathoms ;  and  is  very  common  in  the  Bay  of  Fundy, 
from  low-water  to  50  fathoms. 

This  species  is  closely  allied  to  P.  ptdchella  Malmgren,  from  north- 
ern Europe,  but  differs  somewhat  in  the  form  of  the  head,  which  is 
shorter  and  rounder  in  the  latter;  the  branchia?  also  differ  in  form. 

Eusyllis  phosphorea  Verrill,  sp.  nov. 

Plate  VII,  figure  3. 
Body  slender,  elongated,  tapering  gradually  posteriorly.     Head,  in 
alcoholic  specimens,  broader  than  long,  well-rounded  in  front,  the 
posterior  margin  incurved ;  but  in  living  specimens  the  head  is  longer 


40  Smith  and  Hargei — St.  George's  Banks  Dredgings. 

than  broad  and  slightly  narrowed  posteriorly.  Eyes  small,  but  con- 
spicuous, wide  apart,  the  anterior  considerably  farther  apart  than  the 
posterior  ones.  Palpi  large  in  presex'ved  specimens,  broad  ovate,  and 
well  rounded  anteriorly,  in  contact  at  their  bases;  but  in  living  speci- 
mens more  elongated  and  oblong,  exceeding  the  length  of  the  head. 
Antennffi  (or  tentacles)  long  and  slender,  distinctly  and  rather  regu- 
larly annulated,  but  not  moniliform.  Tentacular  cirri,  in  preserved 
specimens,  similar  to  the  antennae ;  the  upper  ones  are  of  about  the 
same  length,  but  the  lower  are  little  more  than  half  as  long.  Dorsal 
cirrus  of  the  second  segment  is  as  long  as,  or  even  longer  than,  the 
antennoe.  The  dorsal  cirri  on  the  3d,  4th,  and  5th  segments  are 
shorter,  about  equal,  longer  than  the  lower  tentacular  cirrus,  and 
about  half  as  long  as  the  dorsal  cirri  of  the  succeeding  segments,  which 
are  alternately  longer  and  shorter,  the  longer  ones  about  half  as  long 
as  the  breadth  of  the  body.  While  living,  the  alternate  dorsal  cirri 
are  usually  held  extended  and  curled  up  over  the  back.  The  two 
anal  cirri  are  long  and  slender ;  in  one  preserved  specimen  they  ai-e 
more  than  twice  the  breadth  of  the  body,  while  in  the  same  specimen 
the  dorsal  cirri  on  the  second  and  third  segments  preceding  the  anal 
one  are  considerably  longer  than  those  on  the  segments  farther  for- 
ward. 

The  setae  are  all  compound,  rather  long,  mostly  considerably  bent, 
with  a  short,  acute -triangular  terminal  piece,  which  is  very  distinctly 
bidentate  at  the  tip. 

Color  of  body,  when  living,  deep  salmon,  or  light  yellowish  orange, 
with  dark  brown  intestinal  line,  darker  posteriorly  ;  eyes  dark  brown. 

Length,  when  living,  about  25'""';  breadth,  rS""". 

Saint  George's  Bank,  45  fathoms,  among  hydroids;  Bay  of  Fundy, 
off  Grand  Menan,  52  fathoms,  among  hydroids. 

This  species,  when  living,  was  most  brilliantly  phosphorescent, 
with  a  bright  green  light,  so  intense-  as  to  be  distinctly  visible  in 
daylight,  or  close  to  a  large  kerosene  lamp. — A.  E.  V. 

Ninoe  nigripes  Verriii. 

Report  on  the  Invertebrate  Animals  of  Vineyard  Sound,  in  Report  of  U.  S.  Commis- 
sioner of  Fish  and  Fisheries,  part  I,  1873,  p.  595,  1874;  Proceedings  American 
Association  for  Advancement  of  Science,  1873,  p.  382,  pi.  3,  fig.  5,  1874. 

Plate  V,  figure  3. 
Locality  o,  110  fathoms.     Also  Fisher's  Island  Sound,  Vineyard 
Sound,  and  Buzzard's  Bay,  and  waters  outside,  in  8  to  29  fathoms, 
mud;  Casco  Bay,  10  to  68  fathoms;  off  the  coast  of  Maine,  at  various 
depths  to  107  fathoms. 


Smith  and  Harger — St.  George's  Banks  Br  edgings.  41 

Leodice  vivida  Verriii. 

Eunice  vivida  Stimpson,  Marine  Invertebrata  of  Grand  Manan,  p.  35,  1853. 

Leodice  vivida  Verrill.  American  Journal  of  Science,  III,  vol.  v,  p.  9,  January,  1873. 

Plate  V,  figure  5. 
Nothria  conchylega  Maimgren. 

OnupMs  conchylega   Sars,  Beskrivelsir  og   lagttagelser,  p.   61,   pi.   10,  fig.  28  {teste 

Maimgren),  1835. 
Onuphis  Eschrichti  (Ersted,  Gronlands  Annulata  Dorsibranchiata,  p.  20,  pi.  3,  figs. 

33-41,  45,  1843. 
Northia  conchylega  Johnston,  Catalogue  of  British  "Worms,  p.  138,  1865. 
Nothria  conchylega  Maimgren,  Annulata  Polychseta,  p.  66,  1867. 

Plate  VII,  figure  3. 

This  species  is  abundant  in  the  deeper  waters,  especially  upon  hard 
bottoms,  on  the  whole  northern  coast  of  Xew  England,  and  in  the 
Gulf  of  St.  Lawrence.  Maimgren  records  it,  in  30  to  250  fathoms, 
fnmi  Greenland,  Spitzbergen,  Finmark,  and  the  coast  of  Norway. 

The  name  "  Nothi'ia  "  was  substituted  for  Northia  (Johnston)  by 
Maimgren  for  reasons  that  are  scarcely  sufiicient.  The  latter  name 
was,  however,  previously  in  use  for  a  genus  of  shells  (Gi'ay,  1847), 
and  must  be  rejected  on  that  account. 

Nothria  opalina  Ven-iii. 

American  Journal  of  Science,  III,  vol.  v,  p.  102,  1873. 

Plate  VII,  figure  4. 
Body  long  and  slender,  narrowed  anteriorly,  much  depressed  and 
of  nearly  uniform  width  throughout  most  of  its  length  ;  the  five  ante- 
rior segments  much  longer  than  the  others.  Palpi  inferior,  rather 
larcre,  hemispherical ;  antennne  small,  ovate,  close  together,  on  the 
front  of  head.  Three  central  tentacles  very  long  and  slender,  taper- 
ing, acute,  the  basal  portion  regtdarly  annulated  and  thickened  for  a 
considerable  distance,  beyond  which  the  surface  is  smooth,  with  an 
occasional  distant  annulation ;  the  central  odd  one  is  somewhat 
shorter  and  more  slender  than  the  two  adjacent  ones,  which  reach  to 
or  beyond  the  10th  segment ;  outer  pair  much  shorter,  being  less 
than  half  the  length  of  the  central  ones.  Tentacular  cirri  small 
and  very  slender.  Lateral  appendages  or  "feet"  of  the  first  six  se 
tigerous  segments  similar  in  structure  but  more  prominent  than  the 
following  ones,  from  which  they  also  difier  in  having  the  ventral 
cirrus  well  developed,  long  and  tapering,  but  shorter  and  thicker  on 
the  first  segment  than  on  the  five  following.  Those  of  the  first  pair 
have  a  stout  stalk,  which  terminates  in  a  small,  bhuitly  rounded  se- 
tigerous  lobe,  with  a  long,  slender,  subterminal  cirrus-like  lobe  above, 
Trans.  Conn.  Acad.,  Vol.  III.  6  August,  1874. 


42  Smith  and  Harger — St.  George's  Banks  Bredgings. 

longer  than  the  stalk ;  dorsal  cirrus  arising  from  near  the  base,  longer 
and  more  slender  than  the  terminal  cirrus ;  branchial  filament  simple, 
long  and  very  slender,  about  equalling  the  dorsal  cirrus  and  united 
to  it  above  its  base;  ventral  cirrus  ovate,  tapering,  blunt,  arising 
from  near  the  base.  The  second  pair  of  feet  are  similar  to  those  of 
the  first,  except  that  in  the  largest  specimens  there  are  two  branchial 
filaments,  and  the  ventral  cirrus  is  longer  and  more  slender.  The  3d, 
4th,  5th,  and  6th  pairs  have  essentially  the  same  structure,  but  the 
ventral  cirrus  becomes  gradually  longer  to  the  6th,  where  it  is  longer 
than  the  stalk  and  nearly  equal  to  the  terminal  cirrus.  The  succeed- 
ing feet  are  much  shorter ;  the  ventral  cirrus  is  a  mere  conical  papilla, 
which  soon  disappears ;  the  terminal  cirriform  lobe  becomes  smaller 
and  disappears  after  the  10th  pair;  the  branchial  filament  becomes 
larger  and  longer  to  the  middle  region,  where  it  exceeds  in  length 
half  the  diameter  of  the  body,  while  the  dorsal  cirrus  at  the  same  time 
becomes  smaller  and  shorter,  until  it  is  less  than  one-fourth  the  length 
of  the  branchia. 

The  setae  of  the  anterior  feet  consist  of  slender,  acutely  pointed, 
curved  ones,  mixed  with  much  stouter,  blunt  pointed  compound  ones ; 
farther  back  there  are  two  fascicles  of  more  slender  acute  setae,  and 
in  the  lower  bundles  a  few  long,  stout,  bidentate  hooks,  with  a  thin, 
rounded,  terminal  expansion. 

Color,  in  alcohol,  pale  yellowish  white,  but  everywhere  very  bril- 
liantly iridescent,  with  opaline  lustre  and  colors. 

Length,  Y5  to  125"""  ;  diameter,  2*5  to  4""". 

Common  in  110  and  150  fathoms,  haiils  s  and  o.  It  was  also 
dredged  in  1873,  off  Casco  Bay,  in  30  to  94  fathoms,  and  on  Jeffrey's 
Bank,  in  79  to  105  fathoms.  It  was  also  abundant,  on  muddy  bot- 
toms in  deep  water,  at  all  the  localities  in  the  Gulf  of  Maine  examined 
by  Dr.  Packard  and  Mr.  Cooke  hi  1873. 

G-oniada  maculata  CErsted. 

Ann.  Dan.  consp.,  p.  33,  figs.  16,  23,  91,  95,  97,  98  (t.  Malmgren).       Glycera  viri- 
descens  Stimpson,  Marine  Invertebrata  of  Grand  Manan,  p.  53,  1853. 

North  of  Saint  George's  Bank,  110  and  150  fathoms,  mud  (local- 
ities o  and  s)  ;  Saint  George's  Bank,  20  fathoms  (locality  j).  Off 
Casco  Bay,  30  to  90  fathoms,  mud.  Bay  of  Fundy,  20  to  70  fathoms. 
Common  in  the  Gulf  of  Maine,  60  to  100  fathoms.  Northern  coasts 
of  Europe,  from  Finmark  to  Scotland,  10  to  130  fathoms  (Malmgren). 
—A.  E.  V. 


Smith  and  Harger — St.  George's  Hanks  Dredgings.  43 

Rhynchobolus  capitatus  Verriii. 

Glycera  capitata  (Ersted,  Gronl.  Ann.  Dorsibranchiata,  p.  44,  plate  VII.  figs.  87, 
88,  90-94,  96,  99 ;  Malmgren,  Annulata  Polychseta,  p.  70,  1867  {non  Claparede). 

This  species  is  furuisliecl  with  four  well-developed  jaws,  and  there- 
fore belongs  to  the  genus  Rynchoholus,  as  constituted  by  Claparede. 
The  species  without  jaws,  which  he  refers  to  Glycera.,  must  be  distinct. 

Saint  George's  Bank,  60  fathoms  (locality  e) ;  20  fathoms  (locality 
j)\  110  fathoms  (locality  o)  ;  east  of  Saint  George's,  430  fathoms 
(locality  g).  Greenland,  Iceland,  Spitzbergen,  and  northern  coasts  of 
Europe  to  Great  Britain. — A.  E,  V. 

Samythella  VerriU. 

Body  elongated,  composed  of  about  50  segments,  15  of  which  bear 
fascicles  of  setie;  and  posteriorly  about  35  bear  uncini  only,  but 
have  a  small  conical  papilla  above  the  uncigerous  lobe,  as  in  Melinna  • 
the  uncini  commence  on  the  4th  setigerous  ring.  Branchiae  six,  placed 
side  by  side  in  a  continuous  transverse  row.  Cephalic  lobe  oblique, 
somewhat  shield-shape,  with  a  narrowed  prominent  front.  Buccal 
lobe  shorter.     Tentacles  numerous,  smooth  and  slender. 

This  genus  is  closely  allied  to  Sumytha  of  Malmgren,  in  the  struc- 
ture of  the  head  and  number  of  branchiae,  but  diifers  in  having  a 
much  larger  number  of  segments  (in  this  respect  approaching 
Melinyia)^  and  in  having  only  15  setigerous  segments,  instead  of  17. 

Samythella  elongata  Verrili. 

American  Journal  of  Science,  III,  vol.  v,  p.  99,  1873. 

Body  slender,  composed  of  54  segments  in  the  specimens  examined, 
tapering  regularly  to  the  posterior  end.  Cephalic  lobe  about  as 
broad  as  long,  broadly  rounded  posteriorly,  with  the  postero-lateral 
corners  prominent  and  well  rounded,  the  sides  slightly  incurved  and 
rapidly  narrowing  to  the  front,  which  is  about  half  the  width  of  the 
back,  and  subtruncate,  projecting  forward ;  the  middle  region  is  a 
raised  and  convex  oblong  area  as  wide  as  the  front  edge,  into  which 
it  runs.  Buccal  lobe  a  little  shorter.  Tentacles  numerous,  slender, 
tapering.  Branchia?  subequal,  slender,  tapering,  about  twice  the 
length  of  the  cephalic  lobe.  Setse  numerous  and  long  in  all  the  fas- 
cicles except  the  first  three,  the  longest  nearly  one-third  the  diameter 
of  the  body.  The  posterior  end  of  the  body  is  surrounded  by  about 
eight  small  papilloe,  of  which  the  two  ujjper  ones  are  largest. 

Length  of  largest  specimen,  in  alcohol,  40'"'";  diameter,  2-5  to  3'"'". 

The  tubes  consist  of  a  thin  and  tough  lining,  to  which  a  close  layer 
of  sand,  in  grains  of  moderate  and  nearly  uniform  size,  is  firmly 
cemented. 


44  Smith  and  Marger — ;S'^.  George^  Banks  Dredgings. 

G-rymaea  spiralis  Verriii. 

Am.  Journal  of  Science,  III,  vol.  vii,  p.  407,  fig.  2,  and  plate  V,  fig.  4,  April,  18T4. 
Plate  IV,  figure  1. 

Body  long  and  slender,  spirally  coiled,  composed  Fig.  i.* 

of  over  150  segments,  of  which  about  120  bear  fas- 
cicles of  slender  set:*.  Branchiae  long  filiform,  two 
or  three  times  the  diameter  of  body,  arising  in  three 
clusters  on  each  side,  easily  detached  and  often  par- 
tially absent.  Setae  on  the  first  six  or  seven  seg- 
ments a  little  longer  than  the  following  ones.  Gen- 
eral color  dark  red.  Tube  composed  of  firmly 
cemented  mud  and  sand,  coiled  in  a  double  spiral, 
the  two  halves  revolving  in  opposite  directions. 

Also  dredged,  in  1872,  ofi'  Grand  Menan  Island, 
Bay  of  Fundy,  in  60  fathoms;  and  in  187;^,  off  Casco 
Bay,  in  90  fathoms,  mud  ;  and  in  80  fathoms  on  Jeffrey's  Bank. 

?  Potamilla  neglecta  Maimgren. 

(Efversigt  af  Kongl.  Vet.-Akad.   Forliandlingar,    1865,  p.  401,   plate   27,   fig    84. 
Sabella  neglecta  Sars,  Reise  i  Lofot.  og  Finm.,  p.  83  (t.  Maimgren). 

This  species  was  very  abundant  at  localities  d,  h,  ^,  q,  and  also 
occurred  in  110  fathoms  (locality  o). 

The  tubes  are  long  and  tough,  covered  externally  with  sand.     One 
specimen  from  Le  Have   Bank,  45  fathoms   (locality  A),  had  a  large 
number  of  young  ones  within  the  tube,  adhering  to  its  inner  surface. 
—A.  E.  V. 
SpirorblS  valida  Verrill,  sp.  nov. 

Tubes  much  larger  than  usual  in  the  genus,  round,  strong,  thick, 
opaque,  white,  transversely  wrinkled,  rather  rapidly  enlarging,  sinis- 
tral, or  coiling  in  the  same  direction  with  the  hands  of  a  watch  ;  in 
some  specimens,  found  attached  to  flat  shells,  the  tubes  form  low, 
rapidly  enlarging  spirals  of  several  turns,  the  last  whorl  enveloping 
and  concealing  the  others  externally,  except  near  its  termination, 
where  it  rises  obliquely  upon  the  preceding  one,  but  leaving  a  broad, 
shallow  umbilicus  in  which  the  previous  whorls  are  visible ;  in  other 
specimens,  attached  to  convex  univalve  shells  {Turritella  erosa,  etc.), 
the  whorls  rest  upon  the  upper  side  of  each  of  the  preceding  ones, 
forming  an  elevated  and  often  somewhat  irregular  spiral,  increasing 
in  size  upward,  with  a  small  umbilicus,  and  usually  with  the  last  part 
of  the  upper  whorl  slightly  free  from  the  preceding  one  and  ascending 


*  Tube  of  Grymoea  spiralis,  natural  size. 


Smith  and  Harger — St.  George's  Banks  Bredglngs.  45 

obliquely.     Diameter   of  the   larger   tubes,  at   end,  1-75"""  to  2"""; 
height  of  the  more  elevated  spirals,  3'""'  to  5""". 

There  are  15  large  branchiae  in  the  adult  specimens  :  8  on  the  left 
side,  7  on  the  right,  with  the  operculum ;  the  pinnae  are  long,  slender, 
extending  to  near  the  ends  of  the  branchiae,  which  have  slender  and 
short,  naked  tips.  Operculum  large,  Avhite,  calcareous,  irregularly 
obconic,  obliquely  truncated,  with  the  outer  surface  concave,  the 
dorsal  side  gibbous,  the  margin  slightly  sinuous  but  entire,  except 
for  a  small  notch,  or  emargination,  in  the  dorsal  edge  ;  the  dorsal  por- 
tion is  translucent,  while  the  ventral  portion  is  opaque  and  contains 
small,  round,  ova-like  bodies  ;  the  pednncle  is  rather  sliort  and  stout 
gradually  expanding  into  the  base  of  the  operculum,  but  swollen  in 
the  middle,  on  the  dorsal  side.  Collar,  in  the  specimens  examined, 
considerably  mutilated,  apparently  with  a  sinuous  but  not  revolute 
anterior  margin,  and  with  a  long  posterior  dorsal  point.  The  region 
covered  by  the  collar  bears,  at  least  on  the  left  side,  three  large  fjxs- 
cicles  of  slender,  acute,  yellowish  seta^,  both  above  and  below ;  the 
anterior  fascicles  are  directed  forward,  and  the  upper  anterior  one  is 
larger  than  the  other  fascicles. 

Le  Have  Bank,  45  and  GO  fathoms  (localities  h  and  ^). 

The  size  of  this  species  is  exceptionally  large,  and  the  branchiae  are 
unusually  numerous  for  the  genus  Spirorbis,  to  which  I  refer  it  with 
some  hesitation.  When  living  specimens  can  be  studied  it  may  prove 
to  be  a  new  genus.  It  has,  like  Vermilia,  a  calcareous  operculum, 
but  in  form  and  structure  this  organ  resembles  that  of  some  species 
of  Spiro7'bis. — A.  E.  V. 

?  Spirorbis  nautiloides  Lamarck. 

Anim.  sans  Vert.,  ed.  I,  vol.  v,  p.  359,  1818.     ?  Spirorbis  communis  Quatrefages, 
Histoire  naturelle  des  Anneles,  vol.  ii,  p.  489. 

Plate  IV,  figure  4. 

The  species  figured  agrees  pretty  well  with  that  described  by 
Quatrefages,  but  may  not  be  the  same  as  that  of  Lamai-ck,  which  is 
regarded  by  several  writers  as  synonymous  with  it,  and  by  others 
with  S.  horealis,  the  species  so  abundant  on  Facus  at  low-water  mark, 
on  our  shores. 

The  present  species  is  seldom,  if  ever,  found  at  low-water  mark,  and 
occurs  chiefly  on  stones  and  shells  in  deep  water.  The  tubes  are 
opaque,  white,  cylindrical,  rather  closely  coiled,  the  terminal  portion 
not  erect,  and  the  surface  is  more  or  less  conspicuously  marked  with 
lines  of  growth. 

Abundant  on  the  hard  bottoms  at  Saint   George's  Bank;   Casco 


46  Smith  and  Harger — St.  George's  Banks  Dredging s. 

Bay;  Cashe's  Ledge;  and  in  the  Bay  of  Fimdy,  10  to  106  fathoms. — 

A.  E.  y. 

Protula  media  stimpson. 

Marine  Invertebrata  of  Grand  Manan,  p.  30,  1853. 

Plate  VI. 

This  species  usually  forms  much  contorted  and  irregularly  bent 
tubes,  which  are  cylindrical  and  nearly  smooth,  but  with  irregular 
lines  of  growth. 

North  of  Saint  George's  Bank,  110  fathoms  (locality  o).  Often 
brought  up  by  fishermen  on  Saint  George's  Bank,  attached  to  shells 
and  stones.  Abundant  on  Cashe's  Ledge,  50  to  70  fathoms ;  ofi" 
Grand  Menan,  30  to  50  fathoms  ;  oif  Casco  Bay. — A.  E.  V. 

?  Protula  borealis  Sars. 

Vidensk.  Selsk.  Forhandlinger,  1871,  p.  417  (separate  copies,  p.  14). 

Numerous  empty  tubes  from  the  muddy  bottoms  in  110  and  150 
fathoms  (localities  o  and  s)  diifer  considerably  in  form  from  those  of 
the  P.  media.,  ordinarily  met  with,  and  may  be  this  species,  if  distinct. 
But  they  may,  very  likely,  prove  to  be  only  a  variation  of  the  former, 
due  to  the  muddy  character  of  the  bottom.  The  tubes  are  much  less 
bent  and  contorted,  often  but  slightly  curved,  or  nearly  straight, 
nearly  smooth,  but  with  occasional  ridges  or  folds,  indicating  periods 
of  growth. — A.  E.  V. 

Gephteea. 

Phascolosoma  CSementarium  Verrill  (Quatrefages  sp.). 
American  Journal  of  Science,  III,  vol.  v,  p.  99,  1873 ;  and  Report  upon  the  Inverte- 
brate Animals  of  Vineyard  Sound,  in  Report  of  U.  S.  Commissioner  of  Fish  and 
Fisheries,  part  I,  1873,  p.  627,  pi.  xviii,  fig.  92,  1874. 

Very  common  on  the  coast  of  New  England,  from  Long  Island 
Sound  northward,  in  5  to  430  fathoms,  in  dead  univalve  shells. 

Phascolosoma  tubicola  Verriii. 

American  Journal  of  Science,  III,  vol.  v,  p.  99,  1873;  Proceedings  American  Asso- 
ciation for  Advancement  of  Science,  1873,  p.  388,  1874. 

Body  versatile  in  form ;  in  contraction  short,  cylindrical,  oval  or 
fusiform,  12  to  25'""'  long,  2-5  to  4"""  in  diameter;  in  full  extension 
the  body  is  moi-e  or  less  fusiform,  gradually  tapering  anteriorly  into 
the  long,  slender,  nearly  cylindrical  retractile  portion,  which  is  longer 
than  the  rest  of  the  body,  and  bears,  near  the  end,  a  circle  of  about 
ten  to  sixteen  simple,  slender  tentacles,  beyond  which   the  terminal 


Smith  and  Hurler — St.  George's  Banks  Dredgings.  47 

])ortion  is  often  extended  into  a  short  proboscis,  witli  the  montli  at 
the  end ;  below  the  tentacles  there  is  sometimes  a  dilation,  but  this  is 
without  special  spines  or  granules,  and  like  the  rest  of  the  retractile 
portion  in  texture.  The  posterior  end  of  the  body  is  bluntly  rounded, 
and  the  skin  is  transversely  wrinkled  and  rough,  and  covered  with 
small,  round,  somewhat  raised  verrucas  or  suckers,  to  which  dirt  ad- 
heres, and  at  the  end  nearly  always  bears  from  3  to  8  small,  but 
prominent,  peculiar  bodies,  having  a  slender  pedicle  and  a  clavate  or 
globular  head ;  their  nature  is  doubtful.  (They  may  be  sense-organs, 
but  should  be  examined  on  living  s])ecimens.)  At  about  the  poste- 
rior third  of  the  proper  body  is  an  irregular  zone  of  numerous,  dark 
brown,  hard  chitiuous  hooks,  arranged  in  several  rows,  broad  triangu- 
lar in  form,  with  acute  points  directed  forward  ;  among  the  hooks  are 
also  a  few  suckers ;  the  middle  region  is  covered  with  small,  round, 
slightly  raised  suckers,  which  become  much  more  prominent  and 
crowded  at  the  anterior  end  toward  the  base  of  the  retractile  portion, 
and  have  here  the  form  of  small,  subconical,  elevated  warts,  to  which 
dii't  usually  adheres  firmly ;  the  retractile  portion  is  covered  through- 
out with  minute  conical  verruca?  or  paj^illte,  most  prominent  toward 
the  base. 

In  many  respects  P.  cmmentarium  agrees  very  closely  with  this, 
but  it  has  the  posterior  end  much  smoother,  and  with  less  conspicu- 
ous suckers  ;  the  hooks  are  not  so  numerous,  less  acute,  and  lighter 
colored;  the  anterior  part  of  the  body  has  smaller  and  less  j^rominent 
suckers  or  A'erructe  ;  the  skin  is  lighter  colored,  thinner,  and  more 
translucei^t,  and  there  is  a  zone  bearing  several  rows  of  minute,  slen- 
der, acute,  chitinous  spinules,  a  little  l>elow  the  tentacles. 

Haiils^^  o,  and  s,  85  to  110  fathoms.  It  has  also  been  dredged,  in 
60  to  94  fathoms,  off  Casco  Bay. 

?  Phascolosoma  boreale  Keferstein. 

Beitrage  zur  Anat.  und  syst.  Kentniss  der  Sipimculiden,  p.  206. 

This  species  is  rather  short  and  thick,  obtuse  posteriorly,  nearly 
smooth  to  the  naked  eye,  and  destitute  of  both  hooks  and  distinct 
suckers,  but  the  skin  is  minutely  wrinkled  transversely,  and  covered 
with  almost  microscopic  slender  papillte,  and  is  minutely  specked 
with  dirty  yellowish  brown  ;  the  retractile  i)ortion  is  more  distinctly 
granulated  anteriorly.  The  tentacles  are  rather  numerous,  small,  and 
simple. 

Dredged  also  off  Casco  Bay,  64  fathoms;  Cashe's  Ledge,  50  to  72 
fathoms  ;  and  iii  the  Gulf  of  St.  Lawrence  (Whiteaves). 


48  Smith  and  Harger — St.  George's  J^anks  Dredgings. 

MOLLUSCA. 

Pleurotomella  Packardii  VerriU. 

American  Journal  of  Science,  III,  vol.  v,  1873,  p.  15  (December,  1872). 

Shell  thin,  fragile,  translucent,  pale  flesh-colored,  moderately  stout, 
with  an  acute,  somewhat  turreted  spire.  Whorls  nine  ;  the  apical 
whorls,  for  about  two  and  one-half  turns,  are  nearly  smooth,  regular, 
convex,  chestnut-colored ;  below  this  the  whorls  are  shouldered,  strong- 
ly convex  in  the  middle,  but  with  a  smooth  concave  band  below  the 
suture,  corresponding  to  the  posterior  notch  in  the  outer  lip;  the  whorls 
are  crossed  below  the  sub-sutural  band  by  about  16  strong,  prominent, 
rounded,  somewhat  oblique  ribs,  most  prominent  on  the  middle  of  the 
whorl,  but  not  angulated ;  on  the  last  whorl  these  ribs  become  very 
oblique  below  the  middle,  and  follow  the  curve  of  the  edge  of  the 
lip,  nearly  fading  out  anteriorly ;  the  surface  between  the  ribs  is 
marked  by  faint  lines  of  growth  and  by  fine,  unequal,  slightly  raised 
revolving  lines,  which  pass  over  the  ribs  without  intei-ruption.  They 
become  more  evident  on  the  lower  part  of  the  last  whorl,  and  are 
very  faint  on  the  sub-sutural  band,  which  is  more  decidedly  marked 
by  receding,  strongly  curved  lines  of  growth.  The  aperture  is  rather 
broad  above,  elongated  below,  sub-oval,  outer  lip  very  thin,  sharp, 
prominent  above,  separated  from  the  preceding  whorl  by  a  wide  and 
very  deep  sinus,  extending  back  for  about  one-fifth  of  the  circumfer- 
ence of  the  whorl ;  the  anterior  border  of  the  lip  is  incurved  near  the 
end,  and  obliquely  truncate,  forming  a  short,  straight  canal.  Colu- 
mella simple,  nearly  straight,  its  inner  edge  toward  the  end  sharp, 
and  obliquely  excurved.  No  operculum.  Length,  21  •2"""  ;  breadth, 
11-2'""';  length  of  aperture,  120™'";  breadth  of  same,  5-0""".  The 
absence  of  eyes  and  operculum,  great  size  of  the  posterior  sinus,  and 
character  of  the  apex,  indicate  that  this  shell  represents  a  new  genus. 

One  living  specimen  from  (o)  110  fathoms. 

Ringicula  nitida  Verriii. 

American  Journal  of  Science,  III,  vol.  v,  1S73,  p.  16  (December,  1872). 
Plate  I,  figure  2, 

Shell  small,  white,  smooth,  broad  oval,  with  five  Avhorls,  spire  rap- 
idly and  regularly  tapered,  sub-acute,  shorter  than  the  aperture. 
Whorls  very  convex,  regularly  rounded,  the  sutures  well  impressed  ; 
a  well  marked,  impressed,  revolving  line  just  below  the  suture ;  the 
surface  otherwise  nearly  smooth,  but  with  more  or  less  distinct, 
distant,  microscopic  revolving  lines,  most  distinct  anteriorly.  Aj^er 
ture  somewhat  crescent-sha})ed.     Outer  lip  evenly  rounded,  forming 


Smith  and  Harger — St.  George's  Banks  Dredging s.  49 

the  segment  of  a  circle,  the  border  regularly  thickened,  receding  a 
little  posteriorly,  near  the  suture.  Callus  on  the  body  whorl  narrow, 
nearly  even,  but  a  little  swollen  in  the  middle  and  slightly  raised. 
Columella  stout,  recurved  at  the  end,  with  two  strong,  very  promi- 
nent, equal,  spiral  folds — tlie  anterior  one  projecting  beyond  the  canal, 
with  the  end  rounded.  Length,  4-2"""  ;  breadth,  S'l"""  ;  length  of 
aperture,  2-5 """  ;  breadth  of  aperture,  -11""", 
From  110  and  150  fatlioras  (localities  s  and  o). 

Torellia  vestita  Jeffreys. 

This  shell  in  form  and  size  somewhat  resembles  large  specimens  of 
Margarita  helicina,  but  it  has  a  ciliated  epidermis  resembling  that  of 
Veliitina  laevigata.  The  spire  is  small  and  low;  whorls  four,  the 
last  large,  well  rounded,  forming  the  bulk  of  the  shell.  Suture  deep. 
Umlnlicus  small  and  deep,  somewhat  concealed  by  the  reflected  outer 
edge  of  the  columella,  which  recedes  in  front  and  joins  the  outer  lip 
at  an  obtuse  angle,  forming  a  broad,  shallow,  anterior  emargination ; 
inner  border  of  the  columella  a  little  excavated  near  the  body  whorl, 
slightly  swollen  in  the  middle.  Outer  lip  sharp,  regularly  rounded. 
Epidermis  thick,  greenish,  with  conspicuous  lines  of  growth,  finely 
reticulated  by  raised  revolving  lines,  along  which  arise  numerous 
slender,  but  short,  hair-like  processes.  Shell  beneath  the  epidermis 
white,  nearly  smooth.  Length,  7*5™"^;  breadth,  10™™;  length  of 
aperture,  6'"™  ;  breadth,  4-5""". 

Only  one  specimen,  dead  and  inhabited  by  a  Phascolosoma,  was 
found  in  1872.  Since  this,  however,  during  the  explorations  of  1873, 
it  was  dredged  by  Dr.  Packard  and  Mr.  Cooke,  in  52  to  90  fathoms, 
on  Cashe's  Ledge,  ofl:"  the  coast  of  Maine. 

Stylifer  Stimpsonii  Verriii. 

American  Journal  of  Science,  III,  vol.  iii,  p.  283,  1872. 
Plate  I,  figure  1. 

Shell  white,  short,  swollen,  broad  oval;  spire  short,  rapidly  enlarg- 
ing. Whorls  four  or  five,  the  last  one  forming  a  large  part  of  the 
shell ;  convex,  rounded,  with  the  suture  impressed ;  surface  smooth, 
or  with  faint  striae  of  growth.  Color,  when  living,  pale  orange  yel- 
low.    Length,  about  4™'"  ;  breadth,  3"'". 

Parasitic  on  Strongylocentrotus  Drobachiensis.  In  32  fathoms  oft' 
the  coast  of  New  Jersey  (Capt.  Gedney) ;  60  and  65  fathoms  (e  and 
/),  George's  Banks  ;  8  fathoms  off"  Fisher's  Island,  mouth  of  Long 
Island  Sound. 

Trans.  Conn.  Acad.,  Yol.  III.  7  August,  1874. 


50  Smith  and  Harger — St.  George's  Banks  Dr edgings. 

Astarte  undata  Gould. 

VerriD,  American  Journal  of  Science,  III,  vol.  iii,  pp.  213,  287,  1872;  and  Report 
on  the  Invertebrate  Animals  of  Vineyard  Sound,  in  Report  of  U.  S.  Commissioner 
of  Fish  and  Fisheries,  part  I,  1873,  p.  384,  pi.  29,  fig.  203,  1874. 

Plate  I,  figures  6  to  9. 

The  figures  given  in  Gould's  works  are  scarcely  characteristic  of 
this,  the  most  abundant  species  of  the  northern  coast  of  New  England, 
and  we  here  publish  several  figures,  prepared  by  Professor  Verrill, 
which  more  fully  illustrate  the  different  forms  of  the  species.  The 
name  undata  was  proposed  by  Gould  for  a  form  of  his  Astarte  sid- 
cata. 

Astarte  lens  Stimpson. 

Astarte  crebricostata  G-ould,  Invertebrata  of  Massachusetts,  2d  edition,   edited  by 

Binney,  p.  126,  fig.  440,  1870  (not  of  Forbes,  teste  Verrill). 
Astarte  lens  Stimpson,  MS.,  Gould,  op.  cit.,  p.  127  ;    Verrill,  American  Journal  of 

Science,  III,  vol.  iii,  pp.  213,  287,  1872. 

Plate  I,  figures  4  and  5, 
This  species  seems  to  be  more  exclusively  a  deep-water  form  than 
the  last,  although  the  specimens  dredged  by  us  at  the  localities  {g,  o, 
and  s)  mentioned  are  all  much  smaller  than  the  common  form  of  the 
species  in  the  Bay  of  Fuiuly,  and  may  well  be  regarded  as  a  dwarf 
variety. 

Pecten  pustuloSUS  VerriU. 

American  Journal  of  Science,  III,  vol.  v,  1873,  p.  14  (December,  1872). 

Upper  valve  more  convex  than  the  lower,  a  little  swollen  toward 
the  umbo  ;  length  and  breadth  nearly  equal,  the  margin  diverging 
nearly  at  right  angles  from  the  beak  to  the  middle  of  the  anterior  and 
posterior  borders,  on  each  of  which  tliere  is  an  obtuse  angle,  from 
which  the  outline  of  the  ventral  margin  forms  a  regular  curve,  nearly 
semicircular,  but  a  little  produced  ventrally  ;  the  surface  with  about 
14  radiating  rows  of  relatively  large,  prominent,  round,  hollow  vesi- 
cles, those  in  the  middle  rows  nearly  hemispherical,  while  part  of 
those  of  the  lateral  ones  ai"e  subconical  and  smaller ;  seven  or  eight 
of  the  rows  are  first  developed,  at  a  short  distance  from  the  apex  of 
the  shell,  the  other  ones  afterward  coming  in  between  the  primary 
ones ;  the  rows  are  distant  in  the  middle  and  more  crowded  together 
toward  the  borders;  between  the  rows  of  vesicles  the  surface  is 
marked  by  distant,  fine,  impressed  grooves,  which  pass  between  and 
separate  the  vesicles  ;  on  the  umbos,  above  the  origin  of  the  vesicles, 
the  border  of  the  groove  rises  into  a  thin,  slightly  elevated  lamella. 
Lower  valve  with  fine,  close,  slightly  raised,  concentric  lamellae,  be- 


Smith  and  Harger — St.  George's  Banks  Dredgings.  5 1 

coming  faint  toAvard  the  beak.  Auricles  unoqiuil,,tliat  of  the  upper 
valve  small,  and  a  little  projecting  posteriorly,  much  longer  and  more 
prominent,  with  a  deep,  curved  emargination  anteriorly,  its  surface 
with  concentric  lamellae  and  radiating  rows  of  small,  conical  vesicles  ; 
that  of  the  lower  valve  with  a  deep,  angular  byssal  notch  anteriorly, 
its  surface  with  concentric  lamelhi3  and  faint  radiating  ridges.  Color 
yellowish  white.     Length,  7-5"""  ;  height,  8-0"""  ;  thickness,  2-5""", 

East  of  St.  George's  Banks  {g),  in  430  fathoms,  dead  but  fresh 
valves;  and  north  of  the  Banks,  locality  {s),  150  fathoms,  living. 

Pera  crystallina  VerriU. 

Clavelina  crystallina  Moller,  Naturliistorisk  Tidsskrift,  vol.  iv,  p.  95,  1842. 
Pera  imllucida  Stimpson,  Proceedings  Boston  Soc.  Nat.  Hist.,  vol.  iv,  p.  232,  1852. 
Pera  crystallina  Verrill,  American  Journal  of  Science,  III,  vol.  iii,  p.  213,  pi.  8,  fig. 
9,  1872. 

Plate  VIII,  figure  1. 

This  species  was  described  by  Stimpson  from  specimens,  adhering 
to  stems  Sertidarelkt  polyzonias,  variety  gigantea,  taken  in  30  fathoms 
on  St.  George's  Banks.  Professor  Verrill  records  it  from  Murray 
Bay,  Gulf  of  St.  Lawrence. 

Glandula  arenicola  Verrill. 

American  Journal  of  Science,  III,  vol.  iii,  pp.  211,  288,  1872  ;  Report  on  the  Inver- 
tebrate Animals  of  Vineyard  Sound,  in  Report  of  U.  S.  Commissioner  of  Fish  and 
Fisheries,  1873,  p.  701,  1874. 

This  species,  which  was  dredged  by  us  in  immense  numbers  in  28 
fathoms  (haul  c),  has  also  been  dredged,  by  Dr.  Dawson,  at  Murray 
Bay,  Gulf  of  St.  Lawrence,  by  Mr.  T.  M.  Prudden,  in  Buzzard's  Bay, 
and  off  New  London,  Conn.,  by  A.  E,  Verrill. 

Thyone  scabra  Verriii. 

American  Journal  of  Science,  111,  vol.  v,  p.  100,  1873. 

Thyone  fusus  ?  Verrill,  American  Journal  of  Science,  III,  vol.  v,  p.  14,  1873  (mow 
Koren). 

Body  fusiform,  gi-adually  tapered  behind,  with  a  long,  slender,  pos- 
terior portion,  covered  throughout  with  very  numerous,  rather  rigid, 
slender,  scabrous  papillae ;  skin  rather  rigid,  scabrous  with  small, 
rough  points,  which  project  from  the  plates.  Tentacles  ten  ;  eight 
large  ones  much  elongated  and  arborescently  divided  from  near  the 
base ;  the  two  small  ones  are  very  short,  nearly  sessile,  subdivided 
from  the  base.  The  calcareous  plates  of  the  skin  are  very  flat,  some- 
what imbricated,  irregularly  oval,  triangular,  or  subpolygonal,  with 
an  undulated  or  crenulated  margin,  pierced  by  about  20  to  24  unequal 
round  openings,  tAvo  or  three  central  ones  larger  than  the  rest,  the 


52  Smith  and  Harger — St.  George's  BanJcs  Dredgings. 

interspaces  mostly.as  wide  as  the  pores  ;  from  the  center  of  the  upper 
side  arises  an  open,  slender,  flat,  acute  spinous  process,  composed  of 
two  anastomosing  pieces.  The  plates  of  the  papillae  or  suckers  are 
narrow,  elongated,  bent  into  a  bow-shape,  the  middle  expanded  and 
usually  pierced  by  about  four  pores,  two  of  which  are  larger ;  the 
ends  are  also  usually  dilated  and  pierced  with  small  pores  ;  from  the 
middle  arises  a  flat,  spinous  process,  similar  to  that  of  the  skin-plates, 
but  smaller. 

Length,  in  alcohol,  about  50"""  ;  greatest  diameter,  6  to  9™™ ; 
length  of  longest  tentacles,  7"5™™.  Color  of  pi-eserved  specimens, 
yellowish  brown. 

Localities  o  and  s,  110  and  150  fathoms.  Also  dredged,  in  1873, 
oflT  Casco  Bay. 

This  species  resembles  T.  raphanus  Duben  and  Koren  (Troschel 
sp.)  in  form,  but  the  latter  has  long-stalked  tentacles,  branching  only 
near  the  ends,  and  the  plates  of  the  skin  are  different  in  form,  and  in 
the  perforations,  and  lack  the  spinous  processes  which  give  the  species 
its  rough,  scabrous  surface, 

?  Charybdea  periphylla  Peron  and  Lesueur. 

Verrill,  Report  upon  the  Invertebrate  Animals  of  Vineyard  Sound,  p.  724,  1874. 

This  species,  originally  described  and  figured  by  Peron  and  Lesueur 
from  mutilated  specimens  taken  under  the  equator  in  the  Atlantic 
Ocean,  is  doubtfully  identified  b)'  Professor  Verrill  with  a  specimen 
obtained  by  us  east  of  George's  Banks. 

The  body  in  the  alcoholic  specimen  is  elevated,  bell-shaped,  rounded 
above,  with  a  marked  constriction  toward  the  border ;  transparent, 
the  inner  cavity  showing  through  as  a  large,  conical,  dark  reddish 
brown  spot,  with  the  apex  slightly  truncated.  Border  dcejily  divided 
into  sixteen  long,  flat  lobes,  which  are  of  nearly  uniform  breadth 
throughout,  and  slightly  rounded,  or  sub-truncate,  at  the  end  ;  the 
edges  and  end  thin  and  more  or  less  frilled  ;  the  inner  side  with  two 
sub-marginal  carinae.  Eyes  inconspicuous,  but  small  bright  red 
specks  are  scattered  over  the  marginal  lobes.  The  intervals  between 
the  lobes  are  narrow  and  generally  smoothly  rounded,  without  dis- 
tinct evidence  of  the  existence  of  tentacles,  except  that,  in  one  of 
these  intervals,  there  is  a  small  and  short  papilliform  process,  with 
brown  pigment  at  the  base.  The  ovaries  are  mostly  wanting,  but 
portions  are  to  be  seen  as  slightly  convoluted  organs  in  the  mar- 
ginal region,  opposite  the  intervals  between  the  lobes. 


Smith  and  Harger — St.  George's  Banks  Dredging s.  53 

Lafoea  gracillima  G-  0.  Sars  (Alder  sp.). 

Lafoea  fruticosa  Hincks,  History  of  British  Hydroid  Zoophytes,  p.  202,  pi.  41,  fig.  2, 

1868;  and  Annals  and  Magazine  Nat.  Hist,  IV,  vol.  xiii,  pp.  132,  148,  pi.  G,  figs. 

6-10,  pi.  7,  fig.  16.  1874. 
Lafoea  gracillima  G.  0.  Sars  (Alder  sp.),  Bidrag  til  Kundskaben  om  Norges  Hydroi- 

der,  in  Vidensk.-Selskabs  Forhandlinger,  Christiania,  for  1873,  p.  115  (27),  pi.  4, 

figs.  19-21. 

Hincks  reports  this  species  from  100  fathoms  off  the  coast  of 
Iceland,  and  G.  O.  Sars  from  a  depth  of  150  fathoms  off  the  Norwegian 
coast.  It  has  been  dredged  by  Professor  Verrill  in  the  Bay  of  Fundy 
and  in  Casco  Bay. 

Halecium  robnstum  Verrill. 

American  Journal  of  Science,  III,  vol.  v,  1873,  p.  9,  December,  1872. 

Stem  stout  and  coarse,  composed  of  many  tubes ;  branches  stout, 
tapering,  compound  except  at  tips,  pinnately  or  bipinnately  branched, 
the  branchlets  spreading  at  an  angle  of  aboiit  45°  ;  yellowish  white 
and  translucent,  about  '5  of  an  inch  long,  divided  by  simple  distant 
constrictions,  the  long  internodes  usually  bearing  from  two  to  four 
hydroids.  Hydrothecoe  alternate,  large,  deep,  somewhat  vase-shaped, 
with  an  even,  slightly  evei'ted  rim,  below  which  there  is  a  slight  con- 
striction ;  the  middle  region  is  slightly  smaller,  gradually  narrowed 
toward  the  base,  with  a  simple  diaphragm  near  the  base  within. 
The  hydrothecJB  are  articulated  upon  slightly  prominent  projections 
from  the  stem,  in  an  oblique  and  excentric  position,  so  as  to  produce 
a  decidedly  geniculated  appearance.  Most  of  the  hydrothecse  are 
sim^jle,  but  some  have  one  or  two  slightly  pi'ominent  secondary  rims 
near  the  margin.     Height  about  100'"™. 

East  of  St.  George's  Bank,  430  fathoms  (haul  g). 

Sertularella  polyzonias  Gray,  var.  gigantea  Hincks. 

Annals  and  Magazine  Nat.  Hist,  IV,  vol.  xiii,  p.  151,  pi.  7,  figs.  11,  12,  1874. 

Diphasia  mirabilis  Verriii. 

American  Journal  of  Science,  III,  vol.  v,  1873,  p.  9,  December,  1872. 

Stem  stout,  rather  rigid,  narrowed  at  base,  pinnately  branched, 
somewhat  flexuous  between  the  branches,  which  are  alternate,  stout, 
rigid,  straight,  constricted  at  base,  spreading  at  an  angle  of  about 
45°.  Hydrothecae  on  the  main  stem  in  two  rows,  nearly  opposite  ; 
on  the  branches  mostly  in  six  regular  rows,  occupying  all  sides  of  the 
branches,  those  in  the  adjacent  rows  alternating.  The  hydrothecae 
have  large,  appressed,  somewhat  swollen  bases,  but  the  upper  portion 
is  rapidly  narrowed,  prominent  and  curved  outward;  aperture 
strongly  bilabiate,  operculated.     Reproductive  capsules  not  observed. 

Le  Have  Bank,  60  fathoms  (haul  e). 


64  Smith  and  Harger — St.  George's  Banks  Dredgings. 

Pennatula  aculeata  Danieisen. 

Pennatula  aculeata  Danieisen,  Forhandlinger  i  Vedenskabs-Selskabet  i  Cliristiania, 

1858,  p.  25  (teste  Kolliker) ;  VerriU,  loc.  cit.,  p.  100,  1873. 
Pennatula  phosphorea,  var.  aculeata,  Kolliker,  Anatomisch-systematische  Beschrei- 

bung  der  Alcyonarien,  1   Abtheilung,  1  Halfte,  p.  134,  pi.  9,  fig.  73,  1870  (from 

Ahandlungeu  d.  Senckenberg.  Naturf.  Gesellschaft.  Frankfort,  Bd.  vii). 
Pennatula  Canadensis  Whiteaves,  Annals  and  Magazine  of  Natural  History,  IV,  vol. 

X,  p.  346,  November,  1872. 
Pennatula,  near  P.  phospliorea  VerriU,  Am.  Journal  of  Science,  III,  vol.  v,  p.  5,  1873. 

Localities  o  and  s,  110  and  150  fathoms.  Also  dredged  by  Mr. 
Whiteaves  in  200  fathoms  in  the  Gulf  of  St.  Lawrence. 

Virgularia  Lyungmanii  Kolliker. 

Op.  cit,  2  HaKte,  1  Heft,  p.  196,  pi.  13,  figs.  133,  134,  1871;  Verrill,  American 
Journal  of  Science,  III,  vol.  v,  p.  100,  1873 ;  "Whiteaves,  Report  on  a  Second 
Deep-sea  Dredging  Expedition  to  the  Gulf  of  St.  Lawrence,  p.  13,  1873. 

This  species  was  described  by  Kolliker  from  specimens  obtained  in 
30  to  80  fathoms,  among  the  Azores,  by  the  Josephine  Expedition 
sent  ont  by  the  Swedish  government.  It  was  also  dredged  in  1872, 
in  the  Gulf  of  St.  Lawrence,  at  a  depth  of  200  fathoms,  by  Mr. 
Whiteaves. 

Urtlcina  nodosa  Verriii. 

Actinia  nodosa  Fabricius,  Fauna  Groenlandica,  p.  350,  1780. 

Urticina  digitata  Verrill,  Am.  Jour,  of  Science,  III,  vol.  v,  p.  5,  1873  (not  of  MiiUer?). 

This  species  has  been  dredged  also  in  deep  water  off"  Casco  Bay 
(Professor  Verrill),  and  in  the  Gulf  of  St.  Lawrence  (Mr.  Whiteaves). 

Cerianthiis  borealis  Verrill. 

American  Journal  of  Science,  III,  vol.  v,  1873,  p.  5,  December,  1872. 
Plate  II,  figure  5. 

Body  much  elongated,  tapering  gradually  to  the  abactinal  opening, 
the  surface  smooth  but  more  or  less  sulcated  longitudinally. 
Marginal  tentacles  very  numerous  and  unequal,  the  inner  ones 
longest,  in  the  largest  specimens  56'"'"  long,  and  3™"'  in  diameter 
at  base,  gradually  tapering,  acute ;  the  outer  ones  25'""'  and  less 
in  length.  Oral  tentacles  numerous,  crowded  in  several  rows,  in 
the  largest  specimens  about  25"""  long,  slender,  acute.  Color  of 
body  olive-brown  or  dark  chestnut-brown,  sometimes  pale  bluish  or 
purplish  just  below  the  tentacles ;  disk  pale  yellowish-brown ;  space 
within  the  oral  tentacles,  around  the  mouth,  deep  brown,  witli  lighter 
radiating  lines ;  oral  tentacles  pale  chestnut-brown  ;  marginal  ones 
deep  salmon  or  yellowish-brown,  the  longest  usually  barred  tr^s- 
versely  with  six  to  eight  dark  reddish-brown  spots,  each  spot  partially 
divided  along  the  median  line  into  two  lateral  ones ;  part  of  the  tenta- 
cles often  have  flake  white  spots  on  each  side,  at  the  base. 


Smith  and  Harger — St.  Georges  Banks  Dredglngs.  55 

The  two  largest  specimens,  dredged  in  1872,  in  28  fathoms,  east  of 
Grand  Menan,  by  Professor  Verrill,  measured  125"""  across  the 
disk  and  tentacles,  but  their  bodies  were  mutilated.  Entire  ones 
of  much  smaller  size  were  dredged  by  Dr.  Packard  and  Mr.  Cook  in 
110  and  150  fathoms,  soft  muddy  bottom,  hauls  ^s'  and  o.  The  largest 
of  these  was  200'""'  long,  and  like  other  species  of  the  genus, 
iidiabited  a  thick,  tough,  felt-like,  muddj^  tube.  It  was  also  dredged, 
in  1873,  in  Casco  Bay,  from  7  to  94  fathoms.  One  of  these  speci- 
mens, dredged  off  Seguin  Island,  in  70  fathoms,  was  450'"'"  long,  40""" 
in  diameter,  and  175'"'"  across  the  tentacles.  A  small  specimen  has 
been  dredged  in  18  fathoms  off  Watch  Hill,  R.  I. 

Epizoanthus  Americanus  Verriii. 

Plate  VIII,  figure  2. 

This  species  lives  upon  stones  as  well  as  upon  shells  inhabited  by 

Eupagiiriis.     The  specimens  from  430  fathoms  {g)  were  on  stones, 

while   those  from  60  and  65  fathoms   {s  and  /')  were  on  shells.     It 

ranges  from  off  the  coast  of  New  Jersey  to  the  Gulf  of  St.  Lawrence. 

Sponges. 

Most  of  the  sponges  obtained  have  not  yet  been  sufficiently  studied  to 
be  reported  upon,  but  the  two  following  species  are  of  special  interest. 

Hyalonema  longissimum  Sars. 

G.  0.  Sars,  on  some  Remarkal^le  Forms  of  Animal  Life  from  the  Great  Deptlis  off 
the  Norwegian  Coast,  p.  TO,  pi.  6,  figs.  35-i5,  1872. 

Only  a  single  and  somewhat  abnormal  specimen  of  this  remarkable 
species  was  dredged  by  us  in  430  fathoms,  but  it  has  since  been 
dredged  in  considerable  abundance  by  Professor  Verrill,  in  95 
fathoms,  off  Casco  Bay,  and  by  Dr.  Packard  and  Mr.  Cooke  on 
Cashe's  Ledge.*  Mr.  Whiteaves  reports  it  also  from  deep  water  in 
the  Gulf  of  St.  Lawrence. 

TheCOphora   ibla  WyvlUe  Thompson. 

Depths  of  the  Sea,  p.  147,  fig.  2-i,  1873;  Verrill,  American  Journal  of  Science,  III, 
vol.  vii,  p.  500,  pi.  8,  fig.  8,  1874. 

Plate  VII,  figure  1. 
This  species,  first  described  by  Wy  ville  Thompson,  from  specimens 
dredged  in  344  fathoms,  off  the  Shetland  Islands,  l)y  the  Porcupine 
expedition,  and  dredged  by  us  in  50  and  60  fathoms  (hauls  e  and  d), 
has  since  been  dredged  by  Dr.  Packard  and  Mr.  Cook  on  Cashe's 
Ledge  and  Jeffrey's  Ledge  in  the  Gulf  of  Maine. 

*  American  .Tournal  of  Science,  III,  vol.  vi,  p.  440,  1873. 


56  Smith  mid  Sarger — St.  George's  Batiks  Dredging s. 

EXPLANATION  OF  PLATES. 

Plate  I. 

Figure  1. — Stylifer  Stimpsonii  Verrill ;   specimen  from  60  fathoms,  George's  Bank 
(haul  i) ;  enlarged  10  diameters. 

Figure  2. — Ringicula  nitida  Verrill ;  specimen  from  110  fathoms;  enlarged  14  diameters. 

Figure  3. — Entalis  striolata  Stimpson ;  several  views  of  animal,  with  the  foot  in  differ- 
ent states  of  expansion  ;  enlarged  about  1^  diameters. 

Figure  4. — Astarte  lens  Stimpson  ;  adult ;  natural  size. 

Figure  5. — The  same  ;  young  specimen  ;  natural  size. 

Figure  6. — Astarte  undaia  Gould ;  inside  of  valves,  showing  the  hinge  ;  natural  size. 

Figure  7. — The  same  ;  young  specimen  ;  natural  size. 

Figure  8. — The  same  ;  adult  specimen ;  natural  size. 

Figure  9. — Variety  of  the  same  ;  adult  specimen  ;  natural  size. 

Figure  10. — Astarte  elliptica  (Brown) ;  natural  size. 

Figure  11. — Cryptodon  obesus  Verrill;  inside  of  valve  ;  enlarged  3  diameters. 

Figure  12. — Astarie  Baiiksii  lie&ch. ;  natural  size. 

Figure  1  was  drawn  from  nature  by  S.  I.  Smith;    2,  5,  6,  7,  8,  9,  11,  by  Professor 

Verrill ;  3,  by  J.  H.  Emerton :  the  rest  from  Binney's  Gould. 

Plate  II. 

Figure  1. — Sertularia  argentea  Ellis   and   Solander ;    a  branch  bearing  reproductive 

capsules  (gonothecse)  with  the  soft  parts  removed ;  much  enlarged. 
Figure  2. — Alcyonium  carneum  Agassiz ;  three  of  the  polyps  fully  expanded ;  much 

enlarged. 
Figure  3. —  Crista  eburnea  Lamouroux ;  a  cluster  of  branches,  enlarged. 
Figure  4. — The  same  ;  a  branch  bearing  ovicells,  more  highly  magnified. 
Figure  5. —  Gerianthus  borealis  Verrill;  entire  animal  removed  from  its  tube  and  fully 

expanded  ;  about  one-third  natural  size. 

Figures  1  and  2  were  drawn  from  nature  by  Professor  Verrill ;    3  and  4  by  Profes- 
sor A.  Hyatt ;  5  by  J.  H.  Emerton. 

Plate  III. 

Figure  1. — Xenodea  megachir  Smith,  male ;  one  of  the  first  pair  of  legs  with  its  epime- 

ron,  seen  from  the  outside  ;  enlarged  20  diameters. 
Figure  2. — The  same ;  one  of  the  second  pair  of  legs,  seen  in  the  same  position  and 

enlarged  the  same  amount. 
Figure  3. — The  same ;  one  of  the  third  pair  of  legs,  with  its  epimeron  and  gill,  seen 

from  the  outside,  and  showing  the  glandular  organ  within  ;  enlarged  20  diameters  ; 

a,  the  tip  of  the  dactylus,  showing  the  perforation  ;  enlarged  100  diameters. 
Figure  4. — The  same  ;  one  of  the  fifth  pair  of  legs,  with  its  epimeron  and  gOl,  seen 

from  the  outside  ;  enlarged  20  diameters. 
Figure  5. — Stenothoe  peltata  Smith,  female ;  one  of  the  second  pair  of  legs,  with  its 

epimeron,  seen  from  the  outside  ;  enlarged  16  diameters. 
Figure  6. — The  same  ;  one  of  the  fourth  pair  of  legs,  with  its  epimeron,  seen  from  the 

outside  ;  enlarged  16  diameters. 
Figure  7. — The  same;  one  of  the  first  pair  of  legs,  seen  from  the  outside  ;  enlarged  50 

diameters. 
Figure  8. — The  same ;  distal  portion  of  the  propodus,  with  the  dactylus,  of  one  of  the 

second  pair  of  legs,  seen  from  the  outside  ;  enlarged  125  diameters. 
Figure  9. — ScaJpellum  Stroemi  Sars  ;  side  view ;  enlarged  5  diameters. 

All  the  figures  were  drawn  on  wood,  from  alcoholic  specimens,  by  S.  I.  Smith. 


Smith  and  Harger — St.  George's  Banks  Dredgings.  57 

Plate  IV. 
Figure  1. —  Gnjmcea  spiralis  Yerrill;  head  and  anterior  part  of  body  ;  enlarged. 
Figure  2. — Pista  cristata  Afalmgren  ;  head  and  anterior  part  of  l)ody  ;  enhirged. 
Figure  .'i. — Phyllodoce  catemda  Verrill ;  dor.'^al  view  of  anterior  part  of  body  and  liead, 

and  extended  proboscis  :  enlarged  about  4  diameters. 
Figure  4. — ?  SpirorUs  nautiloides  Lamarck  ;  entire  animal ;  much  enlarged. 

All  the  figures  were  drawTi  from  life  hj  J.  H.  Emerton. 

Pl.\te  V. 

Figure  I  — Nephthys  ciliata  Rathke ;  one  of  the  lateral  appendages ;  enlarged  10 
diameters. 

Figure  2. — Lumbriconereis  fragilis  ffirsted ;  anterior  part  of  body  and  head,  dorsal 
view  ;  enlarged  about  G  diameters. 

Figure  3. — Ninoe  nigripes  Verrill ;  one  of  the  lateral  appendages  from  the  middle  })art 
of  the  body  ;  greatly  enlarged. 

Figure  4. — Ammochares  assimilis  Sars  ;  entire  animal ;  enlarged  about  4  diameters. 

Figure  5. — Leodice  vivida\QVT\]\]  head  and  anterior  part  of  the  body  and  12th  seg- 
ment ;  dorsal  view  ;  enlarged  about  4  diameters. 
Figure  1  was  copied  from  Ehlers ;  all  the  others  were  drawn  from  nature  by  J.  H. 

Emerton. 

Plate  VI. 

Protula  media  Stimpson ;  animal  removed  from  the  tube ;  enlarged  4  diameters. 
Drawn  from  life  by  J.  H.  Emerton,  from  a  specimen  dredged  near  Grand  Menan, 
Bay  of  Fundy,  by  Professor  Verrill,  in  1872. 

Plate  VII. 
Figure  1. — Thecophora  ibla  W.  Thompson;  specimen  from  60  fathoms,  Le  Have  Bank 

(haul  i) ;  natural  size. 
Figure  2. — Eusyllis  iJhosplwrea  Verrill ;  anterior  and  posterior  portions  of  the  animal ; 

dorsal  view ;  much  enlarged. 
Figure  .3. — Nothria  conchylega  Malmgren  ;  anterior  portion ;  enlarged. 
Figure  4. — Nothria  opalina  Verrill ;  anterior  portion ;  enlarged. 

Figure  I  was  drawn  from  nature  by  Sherman ;  the  others  from  life  by  J.  H.  Emerton. 

Plate  VIII. 

Figure  1. — Pera  crystallina  Verrill ;  enlarged  3  diameters. 

Figure  2. — Epizoanthus  Americanus  Verrill ;  a  single  polyp  expanded ;  enlarged  about 
6  diameters. 

Figure  3. — Chcetoderma  nitidulum  Loven  ;  entire  animal ;  enlarged  4  diameters. 

Figure  4. — The  same  ;  posterior  portion  with  the  gills  expanded ;    enlarged  24  diame- 
ters. 
Figure  1  was  drawn  from  nature  by  Professor  Verrill ;  the  others  were  drawn  from 

life  by  J.  H.  Emerton. 


ERRATA. 

Page  1,  line  13,  for  Hagerman,  read  Hagenman. 
13,     "    34,     "   capypilare,  read  capillare. 

"  28,    "   19,    '•  Caridon,  read  Caridion. 
35,    "     3,   "  Scapellum,  read  Scalpellum. 

"   58,     "    14,    •'   branches,  read  branchlets. 
"   60,     "    12,    ■■'    Plate  X.  read  Plate  IX. 


56  Smith  and  Sarger — St.  George's  Banks  Dredgings. 

EXPLANATION  OF  PLATES. 
Plate  I. 

Figure  1. — Stylifer  Stimpsonii  Verrill;   specimen  from  60  fathoms,   George's  Bank 
(haul  i) ;  enlarged  10  diameters. 

Figure  2. — Ringicula  nitida  Verrill ;  specimen  from  110  fathoms ;  enlarged  14  diameters. 

Figure  .3. — Entalis  striolata  Stimpson ;  several  views  of  animal,  with  the  foot  in  differ- 
ent states  of  expansion  ;  enlarged  about  1^  diameters. 

Figure  4. — Astarte  lens  Stimpson  ;  adult ;  natural  size. 

Figure  5. — The  same  ;  young  specimen  ;  natural  size. 

Figure  6. — Astarte  undata  Gould ;  inside  of  valves,  showing  the  hinge  ;  natural  size. 

Figure  7. — The  same  ;  young  specimen ;  natural  size. 

Figure  8. — The  same  ;  adult  specimen ;  natural  size. 

Figure  9. — Variety  of  the  same  ;  adult  specimen ;  natural  size. 

Figure  10. — Astarte  elliptica  (Brown) ;  natural  size. 

Figure  11. — Cryptodon  ohesus  Verrill ;  inside  of  valve  ;  enlarged  .3  diameters. 

Figure  12. — Astarte  Banksii  Leach  ;  natural  size. 

Figure  1  was  drawn  from  nature  by  S.  I.  Smith;    2,  5,  6,  7,  8,  9,  11,  by  Professor 

Verrill ;  3,  by  J.  H.  Emerton  ;  the  rest  from  Binney's  Gould. 

Plate  II. 

Figure  1. — Sertularia  argentea   Ellis   and   Solander ;    a  branch  bearing  reproductive 

capsules  (gonothecse)  with  the  soft  parts  removed ;  much  enlarged. 
Figure  2. — Alcyonium  carneum  Agassiz ;  three  of  the  polyps  fully  expanded ;  much 

enlarged. 
Figure  3. —  Crista  eburnea  Lamouroux ;  a  cluster  of  branches,  enlarged. 
Figure  4. — The  same ;  a  branch  bearing  ovicells,  more  highly  magnified. 
Figure  5. —  Cerianthus  horealis  Verrill ;  entire  animal  removed  from  its  tube  and  fully 

expanded ;  about  one-third  natural  size. 

Figures  1  and  2  were  drawn  from  nature  by  Professor  Verrill ;    3  and  4  by  Profes- 
sor A.  Hyatt ;  5  by  J.  H.  Emerton. 

Plate  III. 
Figure  1. — Xenoclea  megachir  Smith,  male ;  one  of  the  first  pair  of  legs  with  its  epime- 

ron,  seen  from  the  outside ;  enlarged  20  diameters. 
Figure  2. — The  same ;  one  of  the  second  pair  of  legs,  seen  in  the  same  position  and 

enlarged  the  same  amount. 
Figure  3. — The  same ;  one  of  the  third  pair  of  legs,  with  its  epiraeron  and  gill,  seen 

from  the  outside,  and  showing  the  glandular  organ  within  ;  enlarged  20  diameters  ; 

a,  the  tip  of  the  dactylus,  showing  the  perforation ;  enlarged  100  diameters. 
Figure  4. — The  same ;  one  of  the  fifth  pair  of  legs,  with  its  epimeron  and  gill,  seen 

from  the  outside  ;  enlarged  20  diameters. 
Figure  5. — Stenothoe  peltata  Smith,  female ;  one  of  the  second  pair  of  legs,  with  its 

epimeron,  seen  from  the  outside  ;  enlarged  16  diameters. 


Smith  and  Haryer — St.  George's  Banks  Dredgings.  5V 

Plate  IV. 
Figure  1. —  Gryrmm  spiralis  Verrill;  liead  and  anterior  part  of  body  ;  enlarged. 
Figure  2. — Pista  cristata  Malmgren  ;  head  and  anterior  part  of  body  ;  enlarged. 
Figure  :5. — Phyllodoce  catenula  Verrill ;  dorsal  view  of  anterior  part  of  body  and  head, 

and  extended  proboscis :  enlarged  about  4  diameters. 
Figure  i. — ?  Spirorbis  nautiloides  Lamarck  ;  entire  animal ;  much  enlarged. 

All  the  figures  were  drawn  from  life  by  J.  H.  Emerton. 

Platb  V. 

Figure  1  — Nephthys  ciliata  Rathke ;  one  of  the  lateral  appendages ;  enlarged  10 
diameters. 

Figure  2. — Lumbriconereis  fragilis  (Ersted ;  anterior  part  of  body  and  head,  dorsal 
view ;  enlarged  about  G  diameters. 

Figure  3. — Nino'e  nigripes  Verrill ;  one  of  the  lateral  appendages  from  the  middle  part 
of  the  body  ;  greatly  enlarged. 

Figure  4. — Ammochares  assimilis  Sars  ;  entire  animal ;  enlarged  about  4  diameters. 

Figure  5. — Leodice  vivida  Verrill ;  head  and  anterior  part  of  the  body  and  1 2th  seg- 
ment ;  dorsal  view  ;  enlarged  about  4  diameters. 
Figure  1  was  copied  from  Ehlers ;  all  the  others  were  drawn  from  nature  by  J.  H. 

Emerton. 

Plate  VI. 

Protula  media  Stimpson ;  animal  removed  from  the  tube ;  enlarged  4  diameters. 
Drawn  from  life  by  J.  H.  Emerton,  from  a  specimen  dredged  near  Grand  Menan, 
Bay  of  Fundy,  by  Professor  Verrill,  in  1872. 

Plate  VII. 
Figure  1. — Thecop}io7-a  ibla  "W.  Thompson ;  specimen  from  60  fathoms,  Le  Have  Bank 

(haul  i) ;  natural  size. 
Fjgure  2. — Eusyllis  pliosphorea  Verrill ;  anterior  and  posterior  portions  of  the  animal ; 

dorsal  view ;  much  enlarged. 
Figure  3. — Nofhria  conchylega  Malmgren ;  anterior  portion ;  enlarged. 
Figure  4. — Nbthria  opalina  Verrill ;  anterior  portion ;  enlarged. 

Figure  I  was  drawn  from  nature  by  Sherman ;  the  others  from  life  by  J.  H.  Emerton. 

Plate  VIII. 

Figure  1. — Pera  crystalUna  Verrill ;  enlarged  3  diameters. 

Figure  2. — Epizoanthus  Americanus  Verrill ;  a  single  polyp  expanded ;  enlarged  about 
6  diameters. 

Figure  3. — Chcetoderma  nitidulum  Loven;  entire  animal;  enlarged  4  diameters. 

Figure  4. — The  same ;  posterior  portion  with  the  gills  expanded ;    enlarged  24  diame- 
ters. 
Figure  1  was  drawn  from  nature  by  Professor  Verrill ;  the  others  were  drawn  from 

life  by  J.  H.  Emerton. 


Errata. 
5,  line  30,  for  Vetumnus,  read  Vertumnus. 
"     9,  last  line,  for  1873,  read  1874. 
"     11,  line  31,  for  virticillata,  read  verticillata. 
Trans.  Conn.  Acad.,  Vol.  III.  8  July,  1875. 


II. — Descriptions  of  New  and  Rare  Species  of  Hypeoids  from 
THE  New  England  Coast.     By  S.  F.  Clark/. 

A 

The  material  for  this  paper  was  gathered  while  at  work  on  the 
Hydroids  hi  the  Museum  of  Yale  College.  This  colleetion  is  mostly 
from  the  New  England  Coast,  and  is  very  large  and  complete. 

Obelia  bictispidata,  sp.  nov. 

Plate  IX,  fig.  1. 

The  stem  is  erect,  slender,  straight  or  nearly  so,  compound,  con- 
sisting of  many  united  tubes  Avhich  gradually  diminish  in  number 
toward  the  top,  varying  in  color  from  a  light  horn,  to  a  light  whitish 
brown,  sparingly  branched,  and  with  three  or  four  annulations  just 
above  the  origin  of  each  •  branch  ;  branches  short,  ascending,  slender 
and  irregularly  arranged,  sometimes  one,  and  often  two  branches 
starting  from  a  node  ;  branches  few,  very  short,  slender  and  ascending. 

Hydrothecre  very  deeply  cainpainilate,  narrow,  tapering  slightly 
toward  the  base,  very  hyaline,  and  with  eight  to  ten  longitudinal 
lines  extending  from  the  distal  extremity  nearly  to  the  base  ;  the 
rim  is  armed  with  very  acute  teeth,  varying  in  number  from  sixteen 
to  twenty- two,  and  arranged  in  pairs,  the  spaces  in  which  the  longi- 
tudinal lines  terminate  being  a  trifle  wider  and  deeper  than  the  alter- 
nate spaces  ;  the  pedicels  supporting  the  hydrothecse  are  long  and 
tapering,  consisting  of  about  fifteen  annulations.  Gonothecfe  un- 
known. 

Height  of  largest  specimens,  about  three  inches  (80"'"^). 

The  specimens  from  which  this  species  is  described  were  taken  in  3-5 
fathoms,  on  the  reefs  near  Thimble  Islands,  Long  Island  Sound,  Sep- 
tember 23, 1874. 

This  species  is  closely  allied  to  0.  Mdentata,  but  is  readily  distin- 
guished from  the  latter  by  its  entirely  diiFerent  habit,  the  narrower 
and  deeper  calycles,  and  by  the  long  tapering  pedicels  upon  which 
the  calycles  are  supported. 

Obelia  bidentata,  sp.  nov. 

Plate  IX,  fig.  2. 
Stems  clustered,  straight  or  slightly  flexuous,  compound,  composed, 
at  the  base,  of  eight  vor  ten  slender,  united  tubes,  varying  in  color 
from  a  light  horn  to  a  dingy  wdiite,  densely  branched,  and  with  three 


6\  F.  Clark  on  Neio  and  Rare  Species  of  Hydro  ids.  59 

or  four  auimliitions  just  al)ove  the  origin  of  each  branch;  mode  of 
branching  irregular,  two  branches  often  starting  from  a  node,  some- 
times an  alternate  arrangement  of  branches  on  opposite  sides  of  the 
stem,  one  branch  at  each  node.  A  few  o\  the  lowest  branches  some- 
times attain  a  considerable  length  and  resemble  the  main  stem,  the 
upper  ones  are  short,  sparingly  branched  and  with  the  pinnae  diverg- 
ing at  a  slight  angle  ;  the  branchlets  and  ends  of  the  branches  are 
simple,  slender,  translucent,  and  very  graceful.  Ilydrothec*  very 
deeply  canipanulate,  tapering  slightly  toward  the  base,  and  with  nine 
to  twelve  longitudinal  lines  extending  from  the  distal  extremity 
nearly  to  the  base;  the  rim  is  ornamented  with  from  eighteen  to 
twenty-four  very  aciite  teeth,  arranged  in  pairs,  the  spaces  in  which 
the  longitudinal  markings  terminate  being  a  trifle  wider  and  deeper 
than  the  alternate  spaces ;  the  pedicels  supporting  the  hydrothecae 
are  usually  short  and  stout,  consisting  of  three  to  six  strong  rings,  but 
some  of  the  hydrothecae  near  the  base  of  the  stem  have  the  pedicel 
slightly  tapering,  and  composed  of  from  ten  to  twelve  annulations. 
GonotheciB  unknown. 

The  largest  specimen  has  a  height  of  about  6  inches  (150'"'"). 

We  have  had  this  species  from  but  one  locality,  Greenport,  Long 
Island,  where  it  was  collected  August  5th,  1874,  in  considerable 
abundance,  on  the  piles  of  the  wharves  at  low^  water, — U.  S.  Fish 
Commission. 

0.  hideiitata  resembles  0.  gelatinosa  in  the  delicacy  and  grace  of 
its  habit,  in  the  flexibility  of  the  compound  stem  and  branches,  and 
in  the  pellucid  whiteness  of  the  upper  portion  of  its  branches  and 
branchlets. 

Campanularia  pygmaea,  sp-  nov. 

Plate  IX,  fig.  9. 

Stem  often  creeping,  with  short,  stout,  coarsely  annulated,  upright 
pedicels,  sometimes  with  one  or  two  short,  annulated  branches,  each 
bearing  a  single  calycle.  Ilydrothecpe  large,  deep  campanulate, 
tapering  slightly  toward  the  base,  and  with  longitudinal  lines  at 
regular  intervals,  extending  down  al)out  one-fourth  the  length  of  the 
calycle ;  the  rim  is  ornamented  with  from  ten  to  fourteen  square-cut 
denticles,  which  are  more  or  less  hollowed  out  above,  and  separated 
by  rather  shallow  evenly  i-ounded  notches,  of  about  the  same  breadth. 
Gonotheca?  unknown.     Height  about  1""". 

Found  gi-owing  on  a  specimen  of  Sertularia  latlusoda,  from  Casco 
Bay,  Maine, — U.  S.  Fish  Commission. 


60  S.  F.  Clark  on  New  and  Rare  Species  of  Hydroids. 

Campanularia  noliformis  McCrady. 

Plate  X,  fig.  5. 

A  few  specimens  of  this  species  were  collected  at  low-water,  near 
Savin  Rock,  in  the  latter  part  of  September,  1  874,  attached  to  Zostera 
marina. 

The  hydrarium  agrees  very  well  with  McC-rady's  description.  We 
were  not  fortunate  enough  to  find  the  gonotheca?. 

This  is  the  first  time  this  species  has  been  recorded  since  McCrady 
described  it  from  the  harbor  of  Charleston,  S.  Carolina,  in  1857. 

Campanularia  calceolifera  Hincks. 

Ann.  and  Mag.  of  Nat.  Hist.,  vol.  viii,  Aug.,  1871,  page  78,  pi.  vi. 
Plate  X,  figs.  7,  8. 

Stem  filiform,  slender,  flexuous,  sometimes  slightly  branched,  ringed 
at  the  base  and  above  the  origin  of  the  branches,  light  horn-coloi', 
with  the  upper  portions  pellucid  white;  branches  short,  curving  out- 
ward, undivided,  and  bearing  but  two  or  three  calycles.  Hydro- 
thecse  alternate,  broadly  campanulate,  deep,  with  a  slightly  everted 
entire  rim,  and  borne  on  annulated  pedicels  of  variable  length,  those 
on  the  upper  portion  of  the  stem  consisting  of  five  to  eight  rings, 
those  near  the  base,  of  twelve  to  twenty.  At  each  bend,  of  the  stem 
a  single  hydrotheca  is  given  otf,  and  tliese  all  ciirving  outward  give 
to  this  species  a  very  gracefu.1  habit.  Gonotheca?  axillary,  borne  on 
pedicels  consisting  of  three  or  four  rings,  largest  at  the  distal  ex- 
tremity and  tapering  gradually  toward  the  base,  with  a  peculiar  in- 
curved coil  or  twist  at  the  distal  end  near  the  opening ;  the  apei*ture 
is  shield-shaped  and  placed  in  a  depression  on  one  side  of  the  distal 
end.  An  internal  membrane  extends  inward  from  the  shield-shaped 
opening  and  terminates  in  a  circular  orifice  near  the  distal  extremity. 
Height  about  one  inch  (25"""). 

Noank,  Conn.,  from  the  bottom  of  an  old  scow,  Sept.  9,  1874,  with 
gonothecse;  piles  of  wharves  at  Woods  Hole,  Mass.,  Aixg.,  1871, 
with  gonothecse — U.  S.  Fish  Commission. 

Hincks'  figures  represent  the  hydrothecae  as  being  more  everted 
than  they  are  in  the  American  specimens  ;  otherwise  they  exactly 
correspond.  This  is  the  first  time  this  species  has  been  recoi'ded 
from  the  American  coast. 


«S,  F.    Clark  on  Keio  ami  Bare  K<pecies  of  Ih/drokU.  ui 

Gonothyraea  tenuis,  sp.  nov. 

Plato  X,  tig.  8. 

Stem  simple,  somewhat  iiexuous,  slender,  and  aniiulated  ahovc  the 
origin  of  each  of  the  numerous  branches,  wliich  are  an-auged  alter- 
nately, some  simple  and  some  compound,  the  latter  l)earing  numerous 
brancldets,  the  lower  branches  sometimes  half  the  length  of  the  main 
stem  ;  base  of  the  stem  and  of  the  lower  branches  light  horn-color, 
the  ui)])er  portions  of  the  same  and  all  of  the  brancldets  jjellucid 
white;  branches  and  branchlets  spreading,  giving  quite  a  bushy  ap- 
pearance to  a  Avell  develo])ed  colony.  Hydrotheca'  variable  in  size, 
deeply  campanulate,  tapering  quite  rapidly  from  a  little  below  the 
middle  to  the  base  ;  the  rim  is  ornamented  with  teeth  which  show 
considerable  variation,  both  in  number  and  in  shape ;  in  some  cases 
they  are  quite  sharj)  and  shallow,  while  on  other  calycles  upon  the 
same  stem  they  are  of  a  castellated  form  and  sometimes  slightly 
emarginate ;  in  number  they  vary  from  ten  to  sixteen;  the  i)edicels 
which  support  the  hydrotheca?  also  vary  greatly,  some  being  com- 
posed of  but  three  or  four  annulations,  others  of  as  many  as  fourteen. 

Gonothecge  axillary,  very  much  elongated,  narrow,  obconic,  taper- 
ing gradually  from  the  distal  to  the  proximal  end,  borne  on  short 
pedicels  of  but  three  to  live  rings  ;  the  nnmber  of  medusa?  holding 
planuhe  contained  in  each  reproductive  capsule  varies  from  two  to 
five  and  the  number  of  planula^  in  each  medusa  varies  to  the  same 
extent ;  the  tentacles  of  the  medusa?  vary  considerably  in  length 
and  in  number,  some  of  them  being  over  half  as  long  as  the  diameter 
of  the  medusa,  Avhile  others  are  not  more  than  one-third  that  length, 
in  number  they  vary  from  eight  to  fourteen.  The  planuliB  at  the 
time  of  liberation  are  regularly  cylindrical,  and  their  length  is  equal 
to  nearly  foiir  times  the  width.  Height  usually  1  to  1-25  inches  (25 
to  38'""^). 

New  Haven,  Conn.,  on  piles  of  Long  Wharf,  June  2nd,  1875,— 
S.  F.  Clark.  Found  in  consideral)le  abundance  at  low-watei',  loaded 
with  reproductive  capsules.  The  large  size  of  the  latter,  together 
with  the  clusters  of  extracapsular  medusa,  make  this  quite  a  showy 
species  for  one  of  such  humble  growth, 

Opercularella  pumila,  sp.  nov. 

Plate  IX,  figs.  3,  4,  5. 
Stem  rather  stout,  erect   or  creeping,   slightly  flexuous,  amudated 
throughout,   sparingly  branched ;   branches   erect,  undivided,  some- 


62  S.  F.  Clark  on  New  and  Rare  Species  of  Hydroids. 

times  attaining  a  considerable  length.  Hydrothecae  largest  in  the 
middle,  tapering  very  slightly  toward  the  base,  rapidly  converging  at 
the  distal  end,  and  supported  on  short  annulated  pedicels,  consisting 
of  three  to  five  rings.  Gonothecje  fusiform,  with  the  tapering  neck 
often  somewhat  elongated ;  length  about  twice  that  of  the  hydro- 
thecffi.  They  contain  one  to  three  small  globular  or  ovate  immature 
raedusoids.  The  pedicels  consist  of  three  to  six  annulations.  In  the 
creeping  form  the  hydrothecre  appear  at  intervals  borne  on  short 
ringed  stalks  consisting  of  about  three  to  six  rings. 

Portland,  Maine,  August,  1873,  with  gonothecae,  on  piles  of  wharves; 
off  Montauk  Pt.,  Long  Island,  5-15  fathoms,  August,  1874, — U.  S. 
Fish  Commission. 

This  species  closely  resembles  O.  lacerata  of  Hincks,  from  which  it 
is  distinguished  by  the  forms  both  of  the  hydrotheca?  and  gonothecae. 
The  hydrothecae  are  also  smaller  than  those  of  0.  lacerata.  As  the 
reproduction  has  not  been  traced  in  this  species,  it  can  only  be  refer- 
red to  the  genus  provisionally.  I  am  inclined  to  think,  from  the 
shape  of  the  gonothecte  and  from  the  fact  that  they  often  contain 
two  or  three  distinct  reproductive  bodies,  that  it  may  not  belong 
under  Opercularella. 

Opercularella  lacerata  Hincks. 

Campanularia  lacerata  Johnston,  Brit.  Zooph.,  p.  Ill,  PI.  xsviii,  fig.  3. 
Opercularella  lacerata  Hincks,  Brit.  Hydr.  Zoopli.,  p.  194,  PI.  xxxix,  fig.  I. 

Plate  IX,  fig.  6. 

Stem  erect,  simple,  slightly  flexuous,  more  or  less  annulated  through- 
out, sparingly  branched  ;  branches  short  undivided.  Hydrothecae 
ovato-fusiform  and  borne  on  short  pedicels  of  but  two  or  three  annula- 
tions; operculum  composed  of  six  to  eight  segments.  Gonothecae, 
of  the  female  colonies,  a  trifle  wider  at  the  distal  end,  and  tapering 
very  slightly  toward  the  base,  supported  on  short  ringed  pedicels  ; 
the  medusoid  (sporosac)  containing  the  planuhi?  is  quite  large,  the 
diameter  being  about  equal  to  the  length  of  the  gonotheca  ;  from 
two  to  five  planulfe  in  each  medusoid. 

New  Haven,  Conn.,  on  piles  of  Long  Wharf,  May  13th,  1875,  with 
extracapsular  medustB. — S.  F.  Clark. 

The  hydrothecae  in  this  species  average  about  one  tliird  larger  than 
those  of  0.  pumila ;  the  segments  of  the  opercula  are  more  deeply 
cleft ;  and  there  are  differences  in  the  form  of  the  gonothecae. 


*S'.  F.  Clark  on  Xew  and  Hare  Species  of  JlydroiiU.  63 

Calycella  syringa  "incks.     Peculiar  variety. 

Plate  X,  figs.  1 ,  2,  3. 

Sertularia  syringa  L'mn.,  Syst.  1311. 

Calicella  syringa  Hiucks,  Oat.  Devon  Zooph.,  23;   Aim.    N.  11.  (3d  .son),  VIIT,  294. 
Calycella  syringa  Hiueks,   Jiritisli  Hydroid  Zoophytes,  Vol.  I,  p.  206,   Plate  xxxix, 
figs.  2,  2a. 

Stem  simple,  creeping,  nearly  smooth.  HydrothecjB  hyaline,  color- 
less or  tinged  with  a  light  horn-color,  cylindrical,  romided  oft"  helow, 
with  an  everted  rim,  to  which  is  attached  an  opercnlnm  consisting 
of  from  five  to  eight  segments  and  supported  on  twisted  j)edicels  of 
considerable  length,  with  eight  to  fifteen  twists;  some  of  the  liydi'o- 
theca'  have  an  addition  in  the  shape  of  a  wide  ring,  ornamented  with 
from  ten  to  fourteen  longitudinal  markings,  which  rises  for  some  dis- 
tance above  the  rim  and  on  the  summit  of  which  there  is  borne 
either  the  operculum  or  another  ring  ;  in  some  cases  there  are  as 
many  as  four  of  these  rings  with  an  operculum  at  the  summit.  The 
opercula  usually  point  upward,  but  are  occasionally  deflected  into 
the  ealycle. 

From  Casco  Bay,  Me.,  9  fathoms, — U.  S.  Fish  Commission. 

Halecium  articulosum,  sp-  nov. 

Plate  X,  fig.  6. 

Stem  dark  brown  and  tapering  gradually,  very  stout,  sparingly 
branched,  compound,  consisting  of  many,  slender,  anastomosing,  ser- 
pentine tubes  ;  branches  short  and  irregularly  arranged  on  all  sides  of 
the  main  stem ;  branchlets  few  and  very  short ;  both  branches  and 
branchlets  are  divided  into  very  short,  stout  internodes  by  distinct 
joints  placed  at  right  angles  to  the  stem  ;  branches  and  branchlets 
simple,  whitish,  delicate,  becoming  more  numerous  toward  the  top  of 
the  stem.  The  internodes  become  shorter  very  gradually  toward  the 
ends  of  the  branches  and  branchlets.  Hydrothecte  alternate,  short 
and  wide,  one  to  each  segment ;  some  of  them  have  a  cup  within  a 
cup,  as  is  so  often  the  case  in  the  species  of  Halecium.  Gonothecje 
borne  in  rows  on  the  upper  side  of  the  pinnae.  The  female  gono- 
thecaj  are  large,  obovate,  and  have  the  opening  on  one  side  and 
nearer  the  distal  than  the  proximal  end ;  the  male  gonothecse  are 
oblong,  subcylindrical,  and,  like  the  female,  are  sessile.  Height  of  the 
largest  specimens,  5  niches  (125'""'). 

Eastern  end  of  Long  Island  Sound,  8-12  fathoms;  Coxe's  Ledge, 
S.  E.  of  Block  Island,  17-21  fathoms;  Casco  Bay,  Maine;  Eastport, 
Me., — U.  S.  Fish  Commission. 


64  S.  v.  Clark  on  New  and  Rare,  Species  of  Ilydroids. 

H.  articulosiini  resembles  H.  pluniosiini^  but  has  a  stouter  habit ; 
the  iuteruocles  are  shorter  and  stouter ;  and  it  may  also  be  dis- 
tinguished by  the  direction  of  the  joints,  at  right  angles  to  the  stem, 
and  by  the  very  wide-mouthed  calycles.  The  female  gonothecse  some- 
what resemble  those  of  M.  Beanii^  but  are  of  a  stouter  build ;  they 
are  relatively  larger  at  the  distal  extremity,  the  orifice  is  differently 
shaped  and  is  differently  situated,  being  nearer  the  distal  extremity. 

Sertularia  argentea  Ellis  and  Soiander,  vaj\  divaricata  nov. 

Plate  X,  fig.  7. 

Stem  simple,  stout,  erect,  straight  or  slightly  flexuous,  of  a  deep 
horn  color,  regularly  jointed,  each  joint  having  two  or  three  branches  ; 
branches  alternate,  sparingly  branched,  diverging  at  right  angles 
from  the  main  stem  and  all  in  the  same  plane,  divided  quite  regularly 
by  joints,  each  bearuig  two  pairs  of  hydrothecte,  much  resembling 
a  young  shoot  of  the  usual  form  of  S.  argentea.  Hydrothecte  nearly 
opposite,  curving  strongly  outwards,  with  a  bilabiate  mouth,  the 
upper  lip  being  considerably  smaller  than  the  lower  ;  hydrothecse  are 
also  scattered  along  the  stem  in  pairs.     Gonothecae  unknown. 

Collected  at  Oasco  Bay,  Me.,  1878, — U.  S.  Fish  Commission. 

I  at  first  thought  that  this  was  a  distinct  species,  but  I  have  since 
had  intermediate  forms  which  prove  quite  conclusively  that  it  is  only 
a  variety  of  S.  argentea.  Considerable  variation  is  shown  in  the 
hydrotliecae  of  this  variety  ;  some  of  them,  on  the  same  stem,  are 
more  directly  opposite  and  curve  outwards  more  than  others. 

Plumularia  Verrillii,  sp.  nov. 

Plate  X,  fig.  9. 

Stems  erect,  simple,  straight  or  slightly  curved,  slender,  two  to 
four  inclies  high,  of  a  bright  horn-color,  branched  and  regularly 
jointed  by  transverse  divisions;  the  branches  have  their  origin  near 
the  base  of  the  stem,  are  ei-ect  and  resemble  the  main  stem  in  all  par- 
ticulars; pinnae  occasionally  branched,  regularly  arranged  on  two 
sides  of  the  main  stem  and  branches,  sej^arated  by  an  angle  of  ninety 
degrees,  composed  of  long  similar  joints,  each  bearing  a  hydrotheca 
and  a  number  of  nematophores ;  occasionally  there  is  an  odd,  intermedi- 
ate joint  bearing  only  one  or  two  nematophores  and  no  hydrotliecae ; 
a  single  pinna  to  each  joint.  Nematophores  sessile,  compound,  large, 
tapering  to  the  base,  with  a  round  cup-like  opening :  there  are  four 
to  six  on  each  hydrotheca-bearing  joint,  one  on  eacli  side  of  the  upper 


S.  K  Clark  on  JVew  mul  Jiare  Species  of  TTydroida.  f55 

edge  of  the  hydrotheca,  two  or  three  between  the  Iiyth-otheca  and 
the  proximal  end  of  the  joint,  and  occasionally  one  at  the  distal  end  ; 
on  tlie  main  stem  there  are  usnally  two  in  each  axil  and  two  or  three 
on  eaeli  joint.  ITydrotlieca^  small,  sliallow,  ahout  equal  in  depth  to 
the  length  of  the  nematophores,  attached  to  the  stem  by  their 
entire  length;  rim  entire.  Gonotheca?  borne  in  the  axils  of  the 
stem  and  of  the  branclied  ])innfe,  sessile,  tapering  at  the  base,  the 
remaining  portion  either  i-egularly  cylindrical  or  slightly  sw^ollen  in 
the  middle;  aperture  large,  terminal.     Height,  2-5  inches  (64"""). 

Eastport,  Maine,  10-20  fathoms,  1868,— A.  E.  Verrill  and  S.  I. 
Smith. 

P.  Verrillil  is  a  beautiful  little,  peHucid,  white  species,  with  a  deli- 
cate, graceful  habit  which  readily  distinguishes  it  from  any  of  the 
forms  now  known  upon  our  coast.  It  is  the  second  genuine  Plumu- 
laria  from  the  New  England  coast,  both  having  been  discovered  by 
Professor  Verrill.  The  previously  described  species  {P.  tenella  Ver- 
rill) was  dredged  in  1871,  off  Gay  Head,  Martha's  Vineyard,  in  10 
fathoms.  It  has  since  been  dredged  in  4-5  fathoms  oif  the  Thimble 
Islands,  near  New  Haven,  Conn.,  and  it  was  also  found  on  the  piles 
at  Greenport,  Long  Island,  August  5th,  1874,  with  gonothecae.  It 
differs  greatly  from  the  present  species  in  the  form  of  the  gonothecae, 
w^hich  are  in  the  shape  of  an  elegantly  curved  cornucopia,  slender  at 
the  base  and  gradually  enlarged  to  the  end,  and  with  a  cluster  of 
nematophores  at  the  base.    The  hydrotbecae  are  also  different  in  form. 


EXPLANATION   OF   PLATES. 

Plate  IX. 

Figure  1.   Ohelia  hicuspidata ;  from  Thimble  Islands. 

Figure  2.   Ohelia  bidentata ;  from  Greenport,  Long  Island. 

Figure  3.   Opercularelld  pumila ;  creeping  form. 

Figure  4.  The  same,  yoimg,  with  stem  erect ;  from  ofiE  Montauk. 

Figure  5.  The  same,  from  Portland,  Me.,  showing  a  more  luxuriant  growth ;  a  and 
c,  the  hydrarium  ;  h,  gonotheca,  enlarged  32  diameters. 

Figure  6.  Opercularella  lacerata ;  a,  hydrarium  ;  b,  gonotheca ;  c,  medusoid ;  d,  un- 
developed planulse. 

Figure  7.   Campanularia  calceolifera ;  from  Noank,  Conn. 

Figure  8.  The  same  ;  a,  hydrotheca  ;  b,  gonotheca ;  from  Noank,  Conn. 

Figure  9.   Campanularia  pygmcea ;  from  Casco  Bay. 

Trans.  Conn.  Acad.,  Vol.  III.  9  July,  1875. 


66  )S.  I^.  (J lark  on  New  and  Rare  ISpedes  of  Hydroids. 

Plate  X. 

Figure  1.  Galycella  syringa ;  from  Casco  Bay,  showing  a  peculiar  variation  in  the 
operculum. 

Figure  2.  The  same,  showing  the  variation  in  the  size  and  shape  of  the  hydrotheeas 
and  in  the  length  of  the  pedicel. 

Figure  3.  The  same,  with  one  secondary  ring. 

Figure  4.    Clytia  Johnstoni,  from  Noank,  Conn. 

Figure  5.   Campanularia  noliformis,  showing  variations  in  the  pedicels. 

Figure  6.  Halecium  articulosum ;  from  Coxe's  Ledge.  A,  a  branch  bearing  both 
hydrothecte  and  gonothecse ;  a,  gonothecas  ;  6,  hydrotheca3.  B,  a  branch  with  hydro- 
thecae  only ;  h,  a  branchlet ;  c,  hydrothecis. 

Figure  7.  Sertularia  argentea,  var.  diva?-icata ;  from  Casco  Bay. 

Figure  8.  Gonothyrcea  tenuis ;  a,  branch  with  hydrothecae ;  h,  gonotheca  with  extra- 
capsular medusa; ;  c,  medusa  with  radiating  tubes  and  tentacles ;  d,  planulse. 

Figure  9.  Plumularia  Verrillii;  a,  branch  showing  hj^drotheca;  and  nematophores 
and  the  arrangement  of  the  joints ;  b,  gonotheca ;  c,  a  single  joint. 


III.    Ox    TIIK    ClIONDUODITE    FROM    Till':    Tll,I,Y-F()STKK    IkOX    MlNK, 

BuKWSTKR,  Kkw  York.     By  Edward  S.  Dana. 


WITH    THREE   PLATES. 


The  interesting  discovery  by  Seacchi,*  of  the  existence  of  three 
types  in  the  crystals  of  the  Yesnvian  huniite,  gives  especial  interest  to 
the  study  of  chondrodite  — a  mineral  identical  with  humite  in  chemi- 
cal composition,  and  yet  very  diiferent  in  appearance,  as  well  as  in 
origin  and  method  of  occurrence.  The  same  subject  of  humite  has 
since  been  more  exhaustively  investigated  by  vom  Kath,f  with  the 
entire  confirmation  of  Scacchi's  views.  These  authors  have  shown  that 
the  crystals  of  humite  are  to  be  divided  into  three  groups,  all  bear- 
ing the  same  relation  to  each  other  in  respect  to  their  lateral  axes, 
while  the  vertical  axis  has  a  distinct  value  for  each  type.  In  other 
words,  the  planes  occurring  upon  a  given  crystal  bear  simple  relations 
to  each  other,  whereas  only  very  complex  symbols  result  when  the 
planes  of  one  type  are  referred  to  the  axes  of  another.  For  a  full 
explanation  of  this  subject  reference  must  be  made  to  the  valuable 
memoirs  al)ove  alluded  to.  It  will  be  sufficient  to  give  as  an  example 
the  symbols  of  the  occurring  pyramids  of  the  r  series  on  the  second 
and  third  types  of  chondrodite  (see  beyond) ;  (1)  as  referred  to  their 
own  axes ;    (2)  as  referred  to  the  axes  of  the  second  type. 


(1 
II. 

•) 

III. 

II. 

(2.) 

III. 

J-2(r') 

^-2(P«) 

4  - 

36  _ 
55-2 

i2(.^) 

1-2  ip^) 

4  - 
--■> 

36  _ 
45-2 

\Mr^) 

\-2{p') 

4  _ 
—  •) 
3  - 

36  _ 
35    ' 

4-2  (H) 

Ui,^) 

4-2 

36  . 
25-2 

\-W) 

36  _ 

r5-2 

8-2  (p8) 

36  _ 

*  rogg.  Ann..  Erg.  Bd.  iii,  161,  1851. 

f  Pogg.  Ann.,  Erg.  Bd.  v,  321,  1871  ;  vi,  385,    1873. 


68    E.  S.  Dana — Chondrodite  from  the  Tilly- Foster  Iron  Mine. 

The  chemical  composition  of  the  three  types  of  humite  has  been 
most  recently  investigated  by  vom  Rath,*  and  although  analyses  lead 
to  somewhat  different  results  in  the  three  cases,  he  concludes  that  in 
composition  they  are  still  essentially  the  same,  and  that  the  cause  of 
the  variation  in  crystalline  form  is  not  to  be  found  in  the  relative 
amount  of  fluorine  present,  as  has  been  often  assumed. 

A  further  remarkable  peculiarity  true  of  two  of  the  three  types  is 
their  hemihcdral  character,  which  is  clearly  set  forth  in  the  memoirs 
referred  to.  These  points  are  alluded  to  here  because  of  their  direct 
bearing  on  the  crystallization  of  chondrodite,  which  forms  the  sub- 
ject of  this  j^aper, 

Chondrodite  was  first  shown  by  Rammelsberg  to  be  identical  with 
humite  in  chemical  composition,  but  its  ci-ystallographic  relation  to  it 
was  not  brought  out  until  the  investigations  of  Kokscharow.  He 
showed,  in  his  "  Materialien  zur  Mineralogie  Russlands,"  vol.  vi,  p.  73, 
1870,  that  the  crystals  from  Pargas,  Finland,  were  identical  in  form 
and  angles  with  type  II  of  humite.  Vom  Rath  has  followed  with  the 
description  of  crystals  from  Nya-Kopparberg,  Sweden,  and  px'oved 
that  the  same  fact  is  true  of  them. 

The  study  of  the  chondrodite  from  the  Tilly-Foster  iron  mine, 
Brewster,  Putnam  Co.,  New  York,  which  I  have  been  able  to  make 
during  the  past  season,  has  shown  that  it,  too,  is  for  the  most  part  iden- 
tical in  crystalline  form  with  type  II  of  humite,  but  that  at  the  same 
time  crystals  exist  belonging  to  type  I,  and  others  which  belong  to 
type  III.  Further  than  this,  the  chemical  composition  of  the  second 
type  crystals,  as  shown  by  an  analysis  by  Mr.  G.  W.  Hawes  (p.  21), 
agrees  with  great  exactness  with  that  of  the  Swedish  mineral  anal- 
yzed by  vom  Rath.  Moreover,  the  detailed  study  of  these  crystals 
has  shown  that  while  they  agree  with  humite  in  the  character  of 
their  hemihedrism,  as  well  as  in  angles,  they  surpass  it  in  the  multi- 
plicity of  secondary  planes.  Thus  a  single  solid  angle  has  been 
observed  M^hich  was  modified  by  fifteen  distinct  and  well-defined, 
though  very  minute,  planes.  This,  as  will  be  seen  when  the  facts 
are  described  in  detail,  implies  a  delicacy  in  the  action  of  the 
crystallogenic  forces  at  work  which  is  unparalleled,  and  sustains  the 
opinion  that  chondrodite,  or  humite,  is  unique  among  mineral  species. 

The  method  of  occurrence  at  the  Tilly-Foster  iron  mine  has  been 
fully  described  by  Prof.  Dana  in  a  memoir  entitled,  "  Serpentine 
pseudomorphs  and  other  kinds,  etc.,"  Journal  of  Science,  viii,  pp.  371, 

*  Pogg.  Ann.,  cxlvii,  246,  18'72. 


E.  S.  Dana — Chondrodite  from  the  Tilly-Foster  Iroti  3Ime.     69 

447, 1874.     It  may  be  of  interest,  liowever,  to  review  tlie  subject  again 
so  far  as  the  chondroilite  itself  is  immediately  concerned. 

The  chondrodite  forms  the  gangue  of  the  magnetite,  being  every- 
where disseminated  through  it  in  varying  [troportions.  In  tlie  parts 
of  the  mine  wliere  the  ore  is  purest  and  perfectly  firm  and  solid, — the 
so-called  "  blue  ore," — the  associated  chondrodite  is  sparsely  sprin- 
kled through  it  in  small  yellow  grains,  showing  no  trace  of  crystal- 
line form.  Occasionally,  however,  the  firmer  ore  contains  the  chon- 
drodite in  very  large  but  im})erfect  crystals,  or  crystalline  masses, 
associated  directly  with  enstatite  and  enveloped  with  dolomite,  which 
have  a  dark,  rich  brown  color,  and  a  brilliant  luster  on  the  fracture. 
A  distinctly  laminated  structure  is  uniformly  ])resent,  which  is  per- 
haps due  to  cleavage  (?)  (See  page  21.)  Isolated  grains  imbedded  in 
dolomite  often  show  traces  of  crystalline  faces,  though  nothing  that 
admits  of  even  approximate  determination.  An  analysis  of  this  vari- 
ety of  the  mineral  gave  Mr.  Breidenbaugh  (Am.  J.  Sci.,  Ill,  vi,  209), 

Si  35-42,  Fe  5-72,  Mg  54-22,  Fl  9-00  =  104-3G;  equivalent  of  oxygen  replaced  by- 
fluorine,  3-79. 

In  the  lai'ger  portion  of  the  mine  as  no-w  opened  the  soft  "  yellow 
ore"  predominates  :  the  chondrodite  is  present  in  it  in  much  larger 
quantities,  and,  like  the  other  minerals  present,  it  has  almost  uni- 
versally suiFered  extensive  alteration.  A  long  list  of  these  products 
of  alteration  has  been  fully  described  by  Prof.  Dana  in  the  memoir 
already  alluded  to.  The  chondrodite  forms  the  main  portion  of  the 
material  taken  out,  and  many  tons  of  this  refuse  matter  are  yearly 
thrown  away.  It  vai'ies  much  in  color,  but  is  generally  of  a  light 
yellow;  it  iisually  has  more  or  less  of  a  soapy  feel  and  shows  a  vari- 
ety of  transition-products  between  the  semi-altered  material  and 
serpentine.  The  chondrodite  in  this  "  yellow  ore"  is  generally  mas- 
sive ;  but  occasionally  fragments  of  large  coarse  crystals  have  been 
found,  some  of  which  measure  five  or  six  inches  in  length.  These 
are  always  more  or  less  altered  ;  moreover,  the  material  of  which 
they  are  formed  is  far  from  homogeneous,  masses  of  magnetite,  and 
also  chlorite,  being  often  enclosed.  Dolomite  is  the  most  constantly 
associated  mineral  and  occurs  in  rhombohedrons  of  considerable 
size ;  these,  as  well  as  the  crystals  of  chondrodite,  are  often  coated 
■with  magnetite. 

Better  crystals  of  chondrodite  than  those  just  mentioned  are  some- 
times found  in  what  Avere  once  cavities  in  this  massive  material. 
Unfortunately  these  have  all  suffered  from  the  general  alteration  and 
now  have  little  or  no  luster,  and  often  are  not  even  smooth.  These 
cavities   are  almost  invariably  filled    with  a   soft  mealy  serpentine, 


70    E.  S.  Dana — Chondrodite  from  the  Tilly-Foster  Iron  Mine. 

which  can  be  cut  out  with  a  knife.  These  crystals  vary  in  size,  being 
sometimes  an  inch  or  two  in  length.  A  crystallographic  examination 
of  them  is  seldom  possible,  but  a  few  of  the  crystals  found  allow  of 
it,  and  the  results  are  described  beyond.  The  form  is  usually  very 
simple,  and  the  color  varies  from  a  deep  red  to  a  light  yellow.  This 
may  be  said  to  be  the  common  method  of  occurrence  at  the  locality. 
Forti;nately,  matei'ial  much  l)etter  adapted  for  crystallographic 
study  also  occurs,  though  this  is  very  rarely  true.  Narrow  veins 
are  sometimes  met  with,  two  or  three  inches  across,  which  were 
originally  lined  with  more  or  less  perfectly  crystallized  chondrodite 
and  also  with  dodecahedrons  of  magnetite,  crystals  of  rijDidolite,  and 
rarely  apatite,  and  then  subsequently  filled  in  with  dolomite.  Where 
this  has  been  the  case  and  the  dolomite  has  remained  intact  the 
chondrodite  has  been  protected  and  the  crystals  have  retained  per- 
fectly their  luster  and  color.  Only  in  a  few  instances  were  the  ciys- 
tals  polished  when  covered  simply  by  a  soft  serpentine.  The  chem- 
ical composition  of  this  chondrodite  is  given  beyond,  after  the 
description  of  the  crystals.  It  has  a  deep,  gai'net-red  color,  and 
a  luster  equal  to  that  of  the  finest  Binnenthal  blende. 

1.  Description  of  Crystals  belonging  to  Type  II. 

The  remark  of  vom  Rath  in  regard  to  the  irregularity  of  form  of 
the  Swedish  chondrodite  is  eminently  true  of  the  Bi'ewster  crystals. 
For  in  the  same  little  group  no  two  are  alike ;  so  that  each  one  de- 
serves and  requires  an  especial  study. 

The  first  point  to  be  determined  was  the  values  of  the  fundamental 
angles.  Some  difficulty  was  found  in  obtaining  these  from  the  fact 
that  many  crystals,  though  faultless  in  luster,  yet  gave  uncertain 
measurements.  This  was  due  to  the  fractured  condition  of  many  of 
the  planes,  which,  though  often  not  very  apparent  at  first  sight,  yet 
gave  rise  to  a  variety  of  reflected  images  in  the  goniometer,  of  which 
no  one  could  be  accepted  as  trustworthy.  All  the  larger  crystals 
show  a  multitude  of  internal  fractures;  and,  where  such  crystals 
have  been  subjected  to  altering  influences,  this  circumstance  has  has- 
tened their  destruction,  and  in  all  cases  the  external  condition  of  the 
planes  has  been  more  or  less  aflected.  The  direction  of  the  fracture 
lines  was  in  most  cases  entirely  irregular,  though  in  a  number  of 
cases  they  were  distinctly  parallel  to  e^{-l-i).  The  presence  of  these 
cracks  gave  the  crystals  the  appearance  of  having  suffered  sudden 
contraction,  by  which  the  planes  had  been  irregularly  drawn  inward, 
forming  re-entrant  angles ;  in  fact,  in  this  respect,  as  in  general 
appearance,  this  chondrodite  might  be  aptly  compared  to  a  resin. 


E.  S.  Dana — C/iondroilitefrom  the  TiUy-Foster  Iron  Mine.     71 

Tlie  smallest  crystals  proved  to  be  free  from  this  cause  of  irregu- 
larity, and  one  of  tliem,  on  which  the  faces  were  exceptionably  bril- 
liant, was  chosen  for  careful  measurement.  It  may  be  added  that  all 
the  nieasui-cnients  were  made  Avith  an  Oertling  goniometer,  pi-ovidod 
with  two  telescopes. 

The  mean  of  30  measurements  of  A  {0=.00\)  on  r'  (—-2^247) 

gave:   135°  18' 50".     The  maxinumi  variation  from  the  mean  given 

was  ±45".     The  mean  of  30  measurements  of  ^  on  (i"|— -^=z205  J 

gave:    140°  55'  48".     Maximum  variation  -4-45". 

These  were  accepted  as  the  fundamental  angles,  and  as  the  agree- 
ment l)etween   the  other  anoles  measured  and  the  calculations  made 


Table  I. 
Ghondrodite. 


Hwmite. 


(7  =  ^(010) 
Calculated. 

A=O(001) 
Measured. 

Calculated. 

A  (v.  Rath) 
Calculated. 

i 

l-l 

Oil 

147° 

32'  39" 

122° 

44'  (ap.) 

122° 

27' 

21" 

122° 

27'  49" 

ea 

2„ 
5" 

205 

90 

*149 

55  48 

149 

58 

48 

e' 

\^ 

203 

90 

135 

59 

136 

1 

17 

135 

52  15 

c'^ 

2-1 

201 

90 

109 

4 

109 

3 

24 

108 

57  50 

r> 

4- 

247 

129 

42   9 

*135 

18  50 

135 

18 

50 

135 

17  40 

r« 

4- 

245 

137 

25  45 

125 

52 

125 

50 

6 

125 

49   0 

^ 

4- 
3^ 

243 

146 

27  42 

113 

25i 

113 

25 

36 

113 

24  45 

r* 

4-2 

241 

154 

2   9 

98 

14 

98 

13 

6 

98 

12  47 

m? 

-5 

641 

125 

43  56 

95 

22 

95 

19 

40 

95 

17  59 

w> 

2 
3 

223 

127 

1  31 

125 

3 

49 

125 

2  47 

«« 

2 

221 

135 

45  24 

103 

11 

103 

10 

4 

103 

9  35 

upon  the  above  basis  proved  to  be  as  close  as  could  be  desired,  hav- 
ing regard  to  the   nature  of  the  plane  in  each  individual  case,  no 


12    MS.  Dana — Chondrodite  from  the  Tilhj-Foster  Iron  Mine. 

attempt  to  correct  them  was  deemed  desirable.  Calculated  from 
these  angles  the  parameters  are  : 

a  (vert.)=l-57236  ;  ^'^l;  c=l-08630; 

and  the  angle  for  the  fundamental  prism  is 

J/s,Z(llO/sllO)==85°  15' 46"  or  94°  44'  14". 

It  may  be  added  that  the  angle  of  A  on  /  behind  (siY)  was  meas- 
ured with  equal  care,  and  found  to  be  135°  18'  40". 

The  preceding  table*  (I)  includes  the  principal  angles  measured  on 
the  same  crystal,  and  also  those  calculated  from  the  above  parame- 
ters ;  in  addition,  the  corresponding  angles  for  humite,  type  II,  are 
also  given,  as  calculated  by  vom  Rath.  The  angles  of  the  maci-o- 
domes  agree  very  closely,  it  will  be  observed,  in  chondrodite  and 
humite  ;  in  the  brachydomes,  on  the  other  hand,  there  is  a  divergence 
of  6  or  7  minutes. 

The  angles  given  in  table  I,  and  also  in  tables  XII,  XIII,  XIV, 
for  types  I  and  III,  are  the  actual  angles.  In  all  the  other  tables, 
however,  the  supplement  (normal)  angles,  as  measured  and  calculated, 
are  uniformly  given.  The  reason  for  this  was  that  these  angles  hav- 
ing special  reference  to  the  sphere  of  projection,  and  being  chiefly  of 
value  in  calculating  with  it,  it  did  not  seem  worth  while  to  change 
them  from  the  form  in  which  they  had  been  used. 

It  is  necessary  to  explain,  also,  the  system  of  symbols  and  let- 
ters here  and  subsequently  employed.  The  fundamental  foi-m  adopted 
is  the  same  as  that  used  in  Dana's  "  Mineralogy,"  and  first  suggested 
by  the  author  of  that  work  in  Am.  J.  Sci.  II,  xiv,  175,  185.  It  is  to 
be  remembered  that  Scacchi  made  the  prism  of  the  r  series  (i.  e.,  «-3) 
the  fundamental  prism,  and  gave  to  the  vertical  axes  lengths,  in  the  ratio 
of  7  :  5  :  9  to  each  other,  for  types  I,  II  and  III  respectively.  Vom 
Rath  followed  him  in  this  latter  respect,  but  for  the  vertical  prism 
took  that  of  the  7i  series  (i.  e.,  7,  or  110  of  Dana).  Prof  Dana  took  a 
modified  view  of  the  relations  of  the  three  forms,  and  chose  for 
the  fundamental  macrodome  in  each  type  the  plane  making  with 
A{  0)  an  angle  of  122°  to  125°  :  thus  on  humite  (vom  Rath),  type  I, 
124°  17',  II,  122°  28',  III,  125°  15'.  In  this  view  the  vertical  axes 
have  one-third  (I),  one-half  (TI)  and  one-quarter  (III)  of  the  lengths 
assumed  by  Scacchi ;  in  other  words,  their  relation  to  each  other  are 


*  Both  the  symbols  of  Naiimann  (in  the  form  used  in  Dana's  "Mineralogy")  and  also 
of  Miller  are  given;  the  signs  belonging  to  each  plane  omitted Jiere,  as  the  relations  of 
the  planes  are  shown  with  sufficient  clearness  on  the  spherical  projection,  Plate  xiii. 


E.  S.  Dana—  Choiidrodite  from  the  IWij- Foster  Iron  Mhic.     7.3 

as  7  :  |:  fl  or  28  :  ;^0  :  27.  Tlie  method  adopted  by  Seacclii  and  vom 
liatli  lias  the  advaiitao-o  of  exi)ressing  the  sinij>lest  })Ossil)le  iminer- 
ical  ratios  between  tlie  three  tyi)es.  It  is  the  view  of  tlie  aiitlior 
above  referred  to,  however,  tliat  the  variation  in  the  anuU'  ot 
^^1-7(01])  is  to  be  regarded  in  tlie  same  light  as  the  variation  in  the 
vertical  axes  of  the  rhoiubohedral  carbonates,  or  in  the  orthorhombic 
sulphates  ;  or  in  other  Avords,  the  three  types  form  an  isoniorjihous 
series,  and  the  variation  observed  is  no  greater  than  is  constantly 
seen  in  analogous  isomorphous  groups.  This  view  seems  to  find  con- 
firmation in  the  crystallographic  relations  of  humite  and  chrysolite,  a 
subject  already  discussed  by  Scacchi,  Rammelsberg  and  vom  Kath, 
Taking  the  fundamental  form,  as  in  Dana's  "  Mineralogy"  (here  i-sz^T" 
of  other  authors),  the  lateral  axes  are  nearly  identical  with  those  of 
humite,  while  the  vertical  axis  (1  •25928  Kokscharow)  has  exactly  the 
ratio  of  -^jj  to  that  of  humite,  type  II,  and  f  to  that  of  humite,  type 
III ;  in  other  words,  we  have  the  ratios  : 

Humite. 


Chrysolite.         III.  I.  II. 

24      :       27     :     28     :     30. 

If  we  adopt  the  vertical  axes  of  Scacchi  and  quadruple  that  of  chry- 
solite, we  obtain 

II.  I.   Chrysolite.  III. 

5:7:8:9 

These  relations  were  in  effect  lirought  out  by  Scacchi  when  he  showed 
that  what  he  called  the  common  fundamental  form  of  humite,  ob- 
tained by  dividing  the  vertical  axes  by  7  (I),  5  (II),  and  9  (III)  re- 
spectively, was  nearly  identical  with  that  accepted  by  him  for  chry- 
solite. This  fact  seemed  to  Rammelsberg  of  so  much  importance  that 
he  proposed  to  refer  all  the  planes  of  humite  to  this  common  funda- 
mental form  ;  and  in  this  he  has  been  folloAved  by  Kokscharow.  The 
result  of  this  will  be  seen  in  the  following  table,  which  gives  the 
symbols  thus  obtained  for  the  two  common  macrodomes  in  each  tyj)e. 


I. 

II. 

III. 

ro  m 

5/1     \ 
§(2'7 

m 

I  0-^) 

1  (!-') 

9 

8  ('-*' 

I  i^-') 

-:  (-) 

Tr.\ns.  Conn.  Acad.,  Vol.  III.  10  July,  1875. 


H    E.  8.  Dana — (Jhoiidrodite  from  the  Tilly-Foster  Iron  Mine. 

It  will  be  seen  from  these  few  examples  that  the  plan  proposed  in- 
troduces a  set  of  common  molecular  axes  at  the  expense  of  all  crys- 
tallographic  simplicity  in  the  relations  of  the  several  planes  of  each 
type.  Moreover,  the  view  of  Rammelsberg  loses  some  of  its  plausi- 
bility, if,  as  shown  by  vom  Rath,  the  vertical  axes  do  not  stand  in 
direct  relation  to  the  amount  of  fluorine  present.  The  view  of  Prof. 
Dana  here  advocated  seems  to  have  the  advantage  of  presenting  all 
the  relations  in  their  most  natural  light. 

It  may  be  added,  as  completing  the  history  of  the  subject,  that 
DesCloizeanx  refers  all  the  humite  planes  to  one,  and  that  the  second, 
type. 

In  regard  to  the  letters  employed,  it  seemed  to  ofler  the  simplest 
solution  of  an  obvious  difficulty  to  retain  all  the  letters  of  Scacchi  for 
the  second  type,  and  for  the  third  to  use  simply  the  corresponding 
Greek  letters  in  the  same  order,  and  for  the  first  type  to  use  the  cor- 
responding capital  letters.  It  was  not  deemed  advisable  to  use  the 
same  letter  for  two  planes,  on  different  types,  which  bore  no  imme- 
diate relation  to  each  other. 


Table  II. 

A=  O(OOl). 


Table  III. 

C=  w(OlO). 


Calcu- 
lated. 

II. 

III. 

IV. 

i' 

\-i 

Oil 

57°  33' 

57°  28' 

ea 

h 

205 

30   4 

el 

h 

203 

43  58f 

e2 

2-1 

201 

70  57 

yi 

4  _ 

247 

44  41 

j44  404 
]  44  40 

44°  37' 

44°  41' 

r" 

4  _ 

245 

54  10 

54  12 

y3 

4  _ 
3-2 

243 

66  34 

i  66  39 
(  66  32 

66  25 

66  35 

^ 

4-2 

241 

81  47 

81  52 

«,! 

2 
3 

223 

54  56 

«,2 

2 

221 

76  50 

rn^ 

el 

2 

641 

84  40 

Calcu- 
lated. 

II. 

III. 

IV. 

32°  27' 

i  32° 
'(  32 

28' 
32 

90 

90 

90 

50  18 

j  50 
1  50 

7 
30 

(  50° 
\  50 

13' 
30 

50°  12' 

42  34 

42 

39 

42 

32 

42  35 

33  32 

j  33 
}  33 

31 
32 

33 

30 

33  27 

25  58 

1  26 
]  25 

0 
57i 

44  14J 

44 

11 

52  58 

54  16 

54 

18 

E.  aS.  Dana — Chondrodlte  from  the  Tilly- Foster  Iron  Mine.     75 

In  the  tables,  II,  III,  IV,  are  given  the  angles  as  measured 
in  a  series  of  crystals  (each  crystal  is  numbered).  They  are  import- 
ant as  showing  how  far  the  angles  are  constant.  Some  considerable 
variations  from  calculated  angles  in  a  few  instances  are  to  be  ex- 
plained by  the  cause  of  irregulai'ity  already  mentioned — the  occur- 
rence of  irregular  fractures  across  the  planes.  In  table  V  are  given 
the  su])plement  angles  calculated  for  all  the  planes  on  e-  and  also  the 
angles  measured  on  the  several  crystals  (as  before  numbered).  The 
angles  ai-e  in  pairs  corresponding  to  201  and  iiOl,  or  3OI  and  201  in 
each  case.     (Compare  the  spherical  projection,  plate  xiii.) 


Table  IV. 

Angles  measured  on  C  =  i-i  (010). 


V. 

VI. 

VII. 

VIII. 

IX. 

X. 

XI. 

XII. 

r\ 

4  _ 

247 

50°  11' 

(  50°  16' 
]  50  16 

50° 
50 

17' 
17 

50° 

12' 

50°  24' 

r^ 

4  _ 

245 

42" 

34' 

(42° 
(42 

20' 
12 

(42  30 
]42  23 

42  28 

j42 
142 

36 
29 

42°  34< 

(  42  38 
]42  36 

r3 

4  _ 
3-2 

243 

33  26 

33  32i 

j  33 
]33 

33 
34 

33 

27 

33  32 

r* 

4-2 

241 

25 

59 

(20 
V26 

1 
0 

25  55 

25 

57 

25 

56i 

26   0 

n^ 

2 
3 

223 

(44 
]  44 

20 
10 

(44 
]44 

26 
14 

44  14 

44 

15 

n- 

2 

221 

52 

57 

52 

55 

52 

52 

m" 

3 
«-2 

641 

54  31 

Of  the  planes  which  occur,  according  to  Scacchi  and  vom  Rath,  on 
type  II  of  humite,  I  have  identified  all  but  m  of  Scacchi  (f-|)  and 
f-e  of  vom  Rath  (f-t).  Of  new  planes  I  have  found  the  following, 
which  fall  in  the  old  vertical  or  horizontal  zones,  and  many  others  to 
be  described  later;  o  (;-2'=2]0),  r  (2-7=021),  ia  (*-i=047),  //3=(|-I= 
025),  ea(f-?=205),  r«(|-5=489)  ;  of  these  the  most  interesting  is  the 
prism  i-2,  as  hitherto  no  prism  has  been  found  on  either  the  2d  or  3d 
types. 

Hemihedrism — The  ])eculiar  hemihedral  character  of  humite  has 
been  alluded  to,  and  it  is  a  little  striking  that  the  crystals  of  chon- 
drodlte should  show  so  entire  a  corres])ondence  to  it.  Taking  the 
same  position  for  the  crystals  as  vom  Rath,  r-  and  r^  appear  uni- 
formly in  the  positive  (or  upper)  quadrants,  r'  and  r^  always  in  the 


76    E.  S.  Dana — Chondrodite  from  the  Tilly-Foster  Iron  Mine. 

Table  V. 

Angles  measured  on  e-  =  2-j  (201  and  201). 


e' 

2 

203 

ri 

4  - 

247 

ri 

4  - 

245 

y3 

4- 

243 

^ 

4-2 

241 

n' 

2 
3 

223 

n^ 

2 

221 

m 

641 

Calculated. 


26°  57'  53' 


S  59  19  58 

■(  87  22  38 

j  59  14  0 

(  82  34  28 


60  30 
76  32 


0 

14 

j  64   2   9 
{  69  51   3 


j  44  38  20 

{  70  20  31 

j  45  45  24 

/  56  42  18 


37  34  34 
42  57  12 


26°  55' 


59  14 


44  34 

45  40 

45  50 


YII. 


59°  33' 
(approx) 

76  26 
64   0 


45  46 
56  42 


IX. 


59°  30' 
59  30 


76  15 
63  57 


56  26 


42  43 
42  32 


26°  51 


59  20 


82  34 


45  42 
56  42 


42  51 


59°  20' 


76  35 


VI. 
26°  59' 


XI. 

64°   0' 


negative  (or  lower)  and  7\^  is  both  +  and  — ,  but  where  occurring 
alone  is  generally  negative;  n'^  is  generally,  and  m^  always,  nega- 
tive. Of  the  brachydomes  it  may  be  said  that  they  are  often  holohe- 
dral,  but  this  is  not  always  the  case.  The  various  figures  on  the  two 
plates  will  show  the  ti-ue  relations  better  than  words.  It  is  to  be  said, 
however,  that  when  the  brachydomes  are  ±  they  are  still  distinguished 
from  each  other  physically.  Thus  the  -f-  series  may  be  largely  devel- 
oped and  rough,  destitute  of  any  semblance  to  polish,  when  the  negative 
series  is  as  lustrous  as  the  pyramidal  planes.  When  e^  (2-?=:20l)  is  only 
once  present  it  is  uniformly  positive.  The  macrodomes  are  always 
holohedral  on  humite ;  here  this  is  sometimes  the  case,  but  there  is  a 
good  deal  of  irregularity  (as  will  be  seen  in  the  figures),  and  this  is 
conspicuous  in  figiire  V  where  i  and  ik  occur  together  and  also  e«,  ?/?, 
and  i. 

Hahit. — With  regard  to  the  general  habit  of  the  crystals,  it  is  inter- 
esting to  note  the  wide  variation  which  is  shown.  Figui-es  1,  2,  0,  9, 
10,  are  intended  to  give  some  idea  of  the  crystals  as  drawn  symmet- 
rically, and  figures  7,  10,  14,  15,  16,  17,  18,  19,  ,  of  their  actual 
a2:)pearance.  As  will  be  seen,  the  figures  are  drawn  with  C(^-^,  010)  in 
front :  this  was  necessary  in  order  to  give  a  true  idea  of  their  real 
appearance.     The  prism  ^-3  is   so  acute  (49^°)  that   when    directed 


E.  S.  Dana — Choudrodite  from  the  T'llli/- Foster  Iron  Jfi/ie.     77 

toward  the  eye  the  projection  gives  it  but  little  width.  As  a  mat- 
ter of  fact  the  crystals  have  C  uniformly  well  developed  and  are 
generally  attached  approximately  by  the  extremity  of  the  bracliy- 
diagonal  axis.  This  having  been  explained,  it  will  be  clear  that  wliilc 
tig.  3  is  an  almost  exact  rei)roduction  of  an  actual  crystal,  Hg.  5,  by 
the  other  method  of  projection,  gives  an  entirely  false  idea  of  its 
ap])carance.  It  is  certainly  true  that  the  latter  method  shows  the 
hemihedrism  in  its  true  light,  but  this  should  not  weigh  against  the 
other  more  important  consideration. 

The  crystals  from  Avhich  the  partial  figures,  7,  10,  16,  17,  were  drawn 
were  united,  along  with  others  quite  as  diverse,  in  one  small  fragment 
only  half  an  inch  in  length.  It  is  to  be  noted  that  figures  14  and  15 
are  really  more  different  than  would  appear  at  first  glance.  The 
crystals  drawn  in  figures  16  and  19  also  occurred  closely  conjoined 
in  the  same  group ;  and  other  examples  might  be  mentioned.  One 
crystal  of  a  very  prismatic  appearance  (when  placed  in  an  inverted 
position)  is  shown  in  figure  1 9. 

Presence  of  minute  />/«>* ^^s. — The  most  remarkable  feature  of  the 
mineral  from  this  locality  is  yet  to  be  mentioned.  I  refer  to  the  mul- 
titude of  minute  planes  which  modify  many  of  the  solid  angles. 
One  single  case  will  be  discussed  in  detail,  as  the  planes  admitted  of 
more  than  usually  exact  determination ;  it  serves  well  to  illustrate 
the  subject.  A  horizontal  projection  of  a  portion  of  the  crystal  is 
shown  in  fig.  14.  The  crystal  itself  was  small,  and  unfortunately  so 
imbedded  in  dolomite  that  it  was  for  the  most  part  rough  and  be- 
yond even  approximate  measurements.  The  part  available  shoAved 
G  (i-1)  faultless;  also  r^  good;  and  less  satisfactory  r^,  r^  and 
r*.  On  the  solid  angle  between  6',  r^  and  r^  a  large  number  of 
miniite  planes  were  observed ;  they  were  so  extremely  small  (all 
covering  a  surface  not  "OS  of  an  inch  in  breadth)  that  any  exact 
measurements  seemed  at  first  hopeless.  They  were  sharply  defined, 
however,  and  brilliant,  and  when  the  attempt  was  made  it  was  found 
that  they  gave  perfectly  distinct  though  fiiint  reflections.  It  may  be 
remarked  here  that  measurements  in  this  case  were  only  made  possi- 
ble by  the  substitution  of  a  cross,  cut  in  tin  foil  and  illuminated  very 
brilliantly  by  a  gas  l)urner,  for  the  ordinary  spider  lines  in  the  second 
telescope — a  device  for  Avhich  I  am  indebted  to  Prof  Schrauf  of 
Vienna.* 

The  measurements  were  all  made  with  the  greatest  care,  though,  as 
will  be  readily  ixnderstood,   the  exact  adjustment  of  planes  so  small 

*  Ber.  Ak.  Wien,  Ixvii,  1873. 


78    E.  S.  Dana — CJiondrodite  fro^n  the  Tilly -Foster  Iron  Mine. 


was  not  an  easy  task.  The  symbols  were  calculated  from  the  angles 
thus  obtained.  But  as  even  then  some  doubt  remained  as  to  the  de- 
gree of  dependence  which  was  to  be  placed  in  them,  the  measure- 
ments were  all  repeated  with  the  same  care  as  before.  Tlie  result 
was  perfectly  satisfactory,  as  the  variation  in  no  case  exceeded  tlie 
probable  error  of  observation  given  to  each  angle  when  measured  for 
the  first  time.  This  variation  in  most  cases  did  not  exceed  ±2'. 
The  following  supplement  angles  were  obtained  for  the  more  promi- 
nent planes:  C /^r'^  gave  33°  33'  (required  33°  32f ) ;  and  C/^r* 
gave  25°  53'  (required  25°  58');  and  r^^r^  gave  31°  31'  (required  31° 
38').  The  following  table  contains  the  angles  for  each  of  these  mi- 
nute planes  as  measured  on  6',  and  r"^  and  also  on  ^-,  itself  one  of 
this  group. 

Table   VI. 


G=i-l{010). 

r3  =  243 

. 

1^=201. 

Meas.   Calc. 

Meas.   Calc. 

Meas.   Calc.  1 

i- 

2-1 

021 

17° 

37' 

17° 

38i 

23° 

58' 

23° 

49' 

+  a;i 

T- 

2-12-7 

22 

9 

21 

53 

31 

4 

31 

12 

8° 

21' 

8°  37' 

+  a;2 

r- 

2-26-9 

12 

55 

12 

58 

29 

32 

29 

27 

6 

36 

1 
6  35 

+  a;^ 

r- 

2-26-7 

10 

34 

10 

30 

30 

37 

30 

42 

8 

50 

8  54 

+  x^ 

34  It 

T  Y 

4-34-'7 

9 

42 

9 

39 

33 

41 

33 

41 

12 

0 

11  53 

-a;" 

¥-- 

I-24-14 

20 

21 

20 

28 

21 

11 

21 

6 

3 

25 

3  24 

-a;5 

13  13 

12  T 

5-13-12 

34 

32 

34 

27 

7 

32 

7 

15 

21 

15 

21   8 

-a;' 

¥- 

ri3-7 

18 

50 

19 

17 

19 

40 

19 

47 

4 

5 

4   3 

-«« 

^:- 

6-24-13 

22 

24 

22 

31 

12 

15 

11 

59 

12 

22 

12  22 

-x^ 

5  15 
2"  Y 

2-15-6 

16 

5 

15 

47 

18 

51 

19 

7 

7 

39 

7  34 

-a;'» 

13  13 

7"T 

4-13-7 

24 

22 

23 

59 

9 

26 

9 

47 

15 

25 

15   3 

-v"- 

25  25 

7 -25 -9 

]8 

54 

19 

2 

14 

45 

14 

38 

14 

40 

14  52 

-t 

-1 

9-24-8 

21 

55 

22 

4 

13 

18 

13 

14 

19 

32 

19  29 

-t 

-1 

291 

11 

43 

12 

13 

23 

31 

23 

14 

-y3 

-¥ 

9-24-1 

18 

45 

19 

5 

25 

34 

25 

27 

K.  S.  Dana — ChondrocUte  from  the  Tilltj- Foster  Iron  Mine.      79 

The  calculated  symbols  are  also  striven  with  the  aii^jles  which  be- 
long to  theui.  It  will  be  noticed  tliat  /- (27  =  021)  is  itself  one  ot 
the  minute  planes  of  the  same  character  as  those  suironndino- 
it,  and  its  presence  gives  a  reality  to  them  whiclj  they  would  not 
otherwise  have,  and  .shows  what  degree  of  reliance  is  to  be  placed  on 
the  angles.     Cases  of  a  similar  character  will  be  noted  hereafter. 

The  symbols  *  calculated  for  this  series  of  ])lanes  are  certainly  not 
simple;  and  yet  a  moment's  consideration  will  sliow  that  this  was 
exactly  what  Avas  to  be  expected.  Crowded  togetlicr  so  closely, 
they  would  be  abnormal  if  occurring  on  crystals  of  any  species,  while 
this  becomes  still  more  true  for  a  mineral  like  chondrodite.  The 
constantly  recurring,  common  planes  have  ratios  which  in  anv 
other  species  Avould  be  considered  next  to  impossible  :  thus,  in  tyj)e 
II,  1 :  -^  :  -i-:  I ;  and  in  type  III,  1,  ^,  ^,  4,  ^,  ^^.  It  is  to  be  noticed 
that  these  are  the  true  ratios  of  the  r  series  of  pyramids,  which  exist 
no  matter  what  change  be  n\ade  in  the  assumed  axes.  It  is  not  sur- 
prising, then,  that  these  secondary  planes  should  themselves  have  sym- 
bols totally  at  variance  with  the  accepted  law  of  simplicity  of  the 
indices.  Many  cases  of  planes  with  what  may  be  called  abnormal 
indices  have  been  described,  but  frequently  they  are  to  be  explained 
as  has  been  done  by  Brezina  in  the  case  of  the  f|--7  (25-0'24),  which  he 
proved  to  exist  in  wiserine,  as  a  tendency  to  a  plane  Avith  a  simjjle 
index  (1-7=101),  which  has  resulted  in  a  plane  Avith  approximately 
the  given  index.     The  case  in  hand,  hoAvever,  is  quite  different. 

It  will  be  noticed,  hoAvever,  that,  laAvless  as  they  appear  at  first, 
there  is  an  attempt  at  system  in  the  symbols  given.  Thus  in  the 
ratio  of  the  brachydiagonal  to  the  vertical  axis,  we  have : 


x' 

12: 

V 

x' 

13  ; 

;    7 

x' 

12  : 

1 

x'" 

13; 

;    7 

y' 

24: 

13 

x' 

26: 

7 

t 

24: 

8 

x' 

26: 

9 

y' 

24: 

1 

x' 

13: 

12 

and  so  on.  The  ratios  for  the  other  axes  might  be  draAs^n  out  in  the 
same  Avay,  but  they  are  already  contained  in  the  symbols  given  in 
the  table.  A  little  surprise  is  felt  at  first  that  the  uniformity  in  ratio 
is  not  greater,  that,  for  instance,  x'^  is  not  2-13*7,  instead  of  2-12"V; 
but  the  measurements  are  too  good  and  reliable  to  allow  of  such  a 

*  In  the  symbols  given  in  the  tables  (i.  e.,  those  according  to  Naumann)  the  dash 
over  the  second  figure,  or  fraction,  has  been  omitted  (in  order  to  simpHfy  the  work  of 
the  printer).  This  has  also  been  done  in  all  the  following  tables,  being  made 
possible  by  the  fact  that  all  these  planes,  with  one  or  two  exceptions,  belong  to  the 
macrodiagonal  series. 


80    E.  K  Dana — Chondrodite  from  the  Tilly-Foster  Iron  Mine. 

supposition.  It  is  to  be  noticed  that  when  ratios  of  this  character  are 
allowed,  a  slight  change  in  the  measured  angle  will  alter  entirely  the 
calculated  index ;  the  liberty  in  this  respect  is  not,  however,  quite  so 
great  as  it  would  stem  at  first  sight  to  be.  For  example,  the  ratios 
t(M)  ^"<^  f(f  f )  approach  pretty  closely  to  each  other,  and  it  might  be  a 
question  which  was  to  be  accepted  as  the  true  ratio  of  the  two  axes 
for  a  certain  plane  ;  and  yet  if  the  ratio  of  one  of  these  axes  with 
the  third  be  unqiiestionably  expressed  in  sevenths,  e.  g.,  f ,  then  there 
seems  little  doubt  but  that  the  ratio  f  is  to  be  accepted,  for  that  would 
give  8*4'7  or  f-2,  while  the  other  supposition  would  give  .35-72'63  or|--^f. 
This  principle  has  been  accepted  in  obtaining  all  the  indices  given  in 
the  following  tables. 

A  remarkable  fact  connected  with  these  planes, — in  fact,  implied  in 
what  has  already  been  said, — is  that  there  is  so  little  tendency  among 
them  to  lie  in  zo^es.  For  example,  cc^,  a-^,  y~  and  y^  lie  very  nearly 
in  a  zone  with  each  other  and  Z^,  and  yet  the  reflections  in  the  gonio- 
meter deny  that  this  is  exactly  true,  while  no  satisfactory  indices 
can  be  obtained  on  this  supposition,  (.e^,  i^  and  y^  are,  however, 
in  a  zone.) 

In  regard  to  these  planes  two  points  are  to  be  noticed.  In  the  first 
place,  the  question  suggests  itself  whether,  if  referred  to  a  common 
fundamental  form  (see  above),  or  to  that  of  either  of  the  other  types, 
the  relations  of  the  planes  would  be  at  all  more  simple.  This  is  an- 
swered in  the  negative,  as  will  be  seen  to  be  necessary  if  the  trial  is 
made,  and  also  evidently  because  planes  whose  normals  make  angles 
of  a  few  degrees  only  with  one  another  can  never  bear  simple  rela- 
tions to  each  other,  no  matter  wliat  axes  be  assumed. 

In  the  second  place,  it  might  be  urged  that  such  ratios  as  those 
above  given  being  accepted,  there  is  no  reason  why  we  should  at- 
tempt to  express  the  relations  of  the  prominent  planes — those  of 
humite,  type  II,  for  example,  with  simple  numbers  (see  above,  page 
7).  But,  as  has  just  been  stated,  the  attempt  to  refer  these  planes 
themselves  to  other  axes  leads  to  disastrous  results,  while  further,  as 
has  been  shown,  these  planes  are  truly  secondary  and  subordinate 
and  bear  no  relations  to  other  types  of  the  species. 

This  case  has  l)een  dwelt  ujjon  at  considerable  length,  because  it 
was  believed  that  theoretically  the  existence  of  such  planes  w^as  a 
matter  of  some  interest  and  importance,  and  because  this  single  crys- 
tal offered  opportunities  for  exact  determination  which  did  not  exist 
to  the  same  degree  in  any  other  case.  Almost  all  of  tlie  twenty  and 
more  smaller  crystals  examined  showed  some  of  these  secondary 
planes.    In  some  cases,  however,  there  was  a  tendency  to  rounded  edges 


E.  S.  Dana — Chondroditt  from  the  lllly-FoKfer  Iron  Mine.    81 

without  the  foniiation  of  distinct  planes,  as  is  so  common  in  many 
species  ;  and  then  nothing  of  course  couhl  he  done. 

The  foUowing  tables,  VII,  VIII,  TX,  X,  include  the  measured 
angles,  with  the  symbols  obtained,  and  the  corresponding  angles  be- 
longing to  them,  for  a  considerable  number  of  these  minute  planes. 
Those  occurring  on  each  individual  crystal  are  arranged  together,  be- 
ing expressed  by  the  same  letter,  and  where  the  crystal  has  been 
figured,  this  is  also  indicated.  Upwards  of  one-hundred  of  these 
planes  were  measured,  and  an  attempt  was  made  in  every  case  to  ob- 
tain a  satisfactory  index.     It  was  concluded,  however,  to  discard  the 


Table  VII. 


M 


C=z-i(010,.  1 
Meas.   Calc.  i 

+  6^=24(201). 
Meas.    Calc. 

— o 

8-4 

281 

14° 

6' 

13° 

41' 

79° 

2' 

79°  16' 

— v, 

11  11 
T  5 

5-11-4 

25 

14 

25 

34 

73 

29 

73   7 

-"2 

8  16 
3 '11 

IT-16-6 

33 

50 

34 

5 

64 

40 

64  28 

-«3 

13  5 

4  4 

52-65-20 

37 

7 

37 

19 

60 

0 

59  49 

-Si 

3  15 

Y  16 

I6-15-10 

46 

43 

46 

56 

57 

38 

57  22 

-^ 

5_  5 

357 

46 

4 

46 

21 

81 

35 

80  49 

-h 

9_  9 
14  1 

4-9-14 

46 

57 

46 

58 

87 

7 

87  31 

-«2 

7_7 
9  8 

879 

53 

6 

53 

7 

64 

9 

64   7 

-*3 

13 

Y  Y 

236 

'54 

31 

54 

42 

85 

0 

84  33 

+  h 

Y  _7 

TT  Y 

2-7-11 

45 

47 

45 

57 

92 

46 

93   6 

+  t. 

9  9 

10  2 

2-9-10 

36 

16 

36 

21 

91 

20 

91  44 

-n- 

2 

221 

44 

13 

44 

14i 

56 

45 

56  42 

-c 

9  9 

Y  T 

795 

138 

45 

38 

37 

63 

44 

63  58 

-^ 

15  3 

20-15-4 

50 

58 

51 

6 

46 

13 

46   4 

i' 

\-i 

Oil 

32 

34 

32 

27 

79 

55 

79  54 

+P^ 

1- 

157 

42 

0 

42 

17 

109 

36 

110   7 

-f 

> 

4-20-17 

,29 

1 

41 

29 

44i 

90 

0 

89  58 

Trans.  Conn.  Acad.,  Vol.  III.  1 1 


.July,  1875. 


82    E.  S.  Dana — ChondfrodiU  from  the  Tilly-Foster  Iron  Mine. 

larger  portion  as  untrustwortliy,  retaining  those  which  had  given  the 
best  angles.  It  is  not  pretended  that  the  symbols  deduced  are,  even 
in  the  majority  of  cases,  correct  beyond  question  ;  for  the  angles, 
while  perfectly  reliable  in  some  cases,  are  in  others  somewhat  uncer- 
tain, and  for  reasons  already  explained  this  throws  still  greater  doubt 
over  the  indices  which  calculation  may  produce. 

Table  VIII. 


7  7 

z' 

6  5 

11  11 

2^ 

¥  y 

2^ 

1515 
4  14 

Z^ 

17_17 

25 

^:- 

m 

4 

^ 

5  _5 

c 
•=  1 

7  _  7 
9  5 

r^ 

8_4 
9  3 

675 
5-11-6 
14-15 -4 
4-17-3 
2-10-11 

641 

259 
579 
689 


C=  w(OlO). 
Meas.       Calc. 


40° 

0' 

39° 

52' 

28 

44 

28 

32 

41 

0 

41 

14 

14 

6 

13 

43 

35 

42 

35 

54 

54 

18 

54 

17 

50 

32 

50 

16 

46 

45 

46 

10 

45 

18 

44 

51 

A=  0  (001). 
Meas.       Calc. 


65°    25'65°  51' 

72     13   ,72  15 

■i 

82     45    i82  40 


83     55 


83     44 


55     44    55     28 


84     37 


42 

45 

42 

56 

55 

48 

55 

29 

59 

59 

30 

84     40 


The  group  of  planes  clustered  about  ^^  has  already  been  de- 
scribed. It  is  interesting  to  note  that  in  two  instances  analogous 
groups  were  observed,  of  which  ^(l-i  =  Oil)  was  a  member  (see  fig. 
15),  and  in  two  other  cases  the  common  and  prominent  planes  ^i^  (fig. 
15)  and  vi^  (fig.  17)  were  found  in  the  same  relations.  The  angles 
obtained  for  these  planes  show  conclusively  the  degree  of  dependence 
to  be  placed  on  those  measured  for  the  other  planes.  It  will  be 
remembered  that  in  all  cases  these  planes  were  exceedingly  minute. 

The  fact  already  mentioned,  that  all  of  these  planes  belong  to  the 
macrodiagonal  series,  may  possibly  be  explained  in  part  by  the  fact 
that  it  is  uniformly  that  portion  of  the  crystal  (i.  e.,  near  6',  i  l) 
which  is  exposed  and  well  developed.  There  still  remains  the  fact, 
wliich  will  be  noticed  by  a  glance  at  the  spherical  projection  (plate 
xiii)  and   which  does   not   allow  of  an    analogous  explanation,  that 


E.  S.  Dana — Chondrodite  from  the  Tilly-Foster  Iron  Mine.    83 
Table  IX. 


-■ 

e2=2t(201). 
Meas.   Calc. 

^  =  0  (001). 

Meas.   Calc. 

£ 

i 

1 

4 

012 

047 

51"  50' 
47i-48 

51°  50' 
48   4 

HH 

-3 

1 

^ 

2 

025 

58  18 

57  51 

j-« 

8  _ 

489 

40   6 

40  24 

56° 

42' 

56°  59' 

—  T 

1  _  5 

4-510 

55  45 

55  47 

46 

7 

44  18 

-^ 

11  11 
10  Y 

711-10 

39  33 

39  32 

63 

23 

63  26 

+  7r 

1  5 

Y  Y 

3-5-10 

54   2 

54  13 

41 

58 

41  55 

hH 

—nV 

5 

2~ 

552 

43  40 

43  42 

79 

33 

79  22 

—n« 

30 

30-30-1 

42  40 

42  39 

89 

7 

89   6 

tliese  minute  planes  almost  always  lie  in  the  negative  (lower)  quad- 
rants ;  this  has  necessitated  the  drawing  of  some  of  the  crystals  in  an 
inverted  position.  The  figures  show,  in  addition  to  planes  mentioned 
in  the  tables,  some  others  for  which  no  symbols  Avere  obtained. 

Table  X. 


C 

=  w(010). 

-e' 

=j.i  (203). 

i 

1-t 

15 

Oil 

32° 

20' 

32° 

27' 

67° 

15' 

67°  16' 

—  Wi 

17  17 

4-15-15 

34 

41 

34 

18 

58 

21 

58  43 

\-A 

10  Y 

6-17-10 

26 

33 

26 

25 

63 

29 

63  37 

1— 1 

> 

3  ^ 

-3 

-W-, 

r' 

134 

41 

34 

42 

3 

52 

45 

52  18 

>> 

1  5 

O 

—  T 

Y  Y 

8  ^ 

4-5-10 

55 

27 

55 

47 

36 

40 

36  37 

—  6 

Y-* 

15  , 

289 

37 

10 

36 

57 

56 

27 

57  21 

-u, 

13-^ 

12 

3-1513 

29 

22 

30 

10 

63 

45 

63   2 

-M2 

u' 

212-11 

31 

8 

31 

6 

62 

55 

63  13 

84    E.  tS.  Dana  —  Choiidrodite  from  the  Tilly-Foster  Iron  Mine. 

Crystals  of  simjyler  habit. — The  crystals  thus  far  described  have 
all  been  of  a  more  or  less  complicated  character.  But  allusion  has 
been  made  to  some  very  simple  crystals,  which  also  deserve  descrip- 
tion. The  distinction  is  in  most  cases  probably  unimportant, 
though  lielieved  to  be  of  interest  at  first.  The  simple  crystals  are 
uniformly  large;  they  are  so  generally  altered,  and  appear  so  differ- 
ently from  their  small  brilliant  relatives,  that  it  was  supposed  that 
they  differed  from  them  at  least  in  the  purity  of  the  original  mate- 
rial, if  not  more  essentially.  One  brilliant  exception,  however,  to  the 
general  rule  in  regard  to  the  altered  condition  of  these  crystals,  in  the 
form  of  an  isolated  crystal  of  faultless  luster,  and  deep  red  color, 
about  f  of  an  inch  in  length,  as  well  as  numerous  examples  of  transi- 
tion products  between  the  altered  and  unaltered  material,  made  it 
probable  that  all  the  crystals  in  question  were  originally  of  the  same 
character.  Some  examples  are  given  in  figures  3,  4  and  5.  The 
angles  could  be  measured  approximately  only  with  a  hand  goniom- 
eter, but  there  is  no  question  that  they,  as  well  as  others,  belong 
to  type  II.     On  one  of  them  ±r  was  observed. 

In  what  has  been  said  exception  must  be  made  in  regard  to  the 
large  coarse  crystals,  and  crystalline  masses,  mentioned  in  the  early 
part  of  this  article,  and  which  are  made  up  of  a  more  or  less  hetero- 
geneous mass  of  chondrodite,  magnetite  and  sometimes  rijjidolite  ; 
some,  at  least,  of  these  last,  belong  to  type  I.     (See  p.  25.) 

Twins. — The  humite  crystals  of  Vesuvius,  as  well  as  the  Swedish 
chondrodite,  has  been  shown  by  vom  Rath  to  possess  so  great  a  ten- 
dency to  twinning  that  it  is  a  little  remarkable  that  the  contrary 
should  be  true  of  the  mineral  from  Brewster.  Figs.  20,  21,  show  the 
only  method  of  twinning  which  has  been  found,  as  well  as  the  only 
distinct  twin-crystal.  The  axis  of  revolution  here  is  the  vertical  axis 
of  the  crystal,  and  the  composition-face  the  basal  plane  A.  Unfor 
tunately  the  crystal  in  question  was  quite  imperfect,  and  all  that  was 
available  is  shown  in  the  figure.  The  plane  H  (/-?=iOO)  gave  no 
reflections,  so  that  all  measurements  were  made  on  e^(that  is  201 
and  201) ;  in  this  case  these  planes  were  similar  in  luster  as  a  result  of 
the  twinning.  A  revolution  of  the  kind  mentioned  (in  a  perfectly 
symmetrical  crystal)  would,  so  far  as  this  half  of  the  crystal  goes,  have 
the  effect  only  of  making  it  holohedral,  giving  no  re-entrant  angles  ; 
but,  in  case  of  any  irregularity,  it  might  give,  as  here,  a  re-entrant 
angle  in  the  planes  which  are  hemihedral  in  their  occurrence. 

The  measurement  of  the  re-entrant  angle  here  observed  gave  for 
*w2^to2,  10°  38' and  10°  40';  required  10°  39'.  The  other  angles 
measured  on  the  same  crystal  are  given  in  the  following  table. 


E.  /S.  Dana — Ghondrodite  from  the  Tilly-Foster  Iron  Mine.    85 
Table  XI. 


e2  =  2- 
Meas. 

I  (201). 
Calc. 

e2=2- 
Meas. 

I  (201). 
Calc. 

m- 

641 

37° 

39' 

37° 

34i' 

42° 

54' 

42° 

57  ' 

m- 

641 

42 

57 

42 

57 

37 

28 

37 

34+ 

m- 

641 

37 

36 

37 

34i 

42 

55 

42 

57 

m- 

641 

42 

57 

42 

57 

37 

33 

37 

34i 

n' 

221 

45 

45 

45 

45 

56 

42 

56 

42 

v? 

221 

56 

44 

56 

42 

45 

45 

45 

45 

ri' 

221 

45 

34 

45 

45 

56 

41 

56 

42 

n' 

22] 

56 

15 

56 

42 

45 

34 

45 

45 

ml 

223 

44 

45 

44 

38 

70 

16 

70 

20 

iti 

223 

44 

48 

44 

38 

f'2 

245 

59 

13 

59 

14 

82 

34 

82 

34i 

ri 

241 

64 

3 

64 

2 

0 

210 

33 

52 

33 

50i 

33 

48 

33 

50^ 

<P 

60-381 

38 

14 

38 

17 

39 

24 

39 

27| 

641 

641 

(1 

11 

4 

31 

4 

25 

6 

31 

6 

36| 

Besides  the  interest  of  the  twin,  a  noteworthy  fact  in  the  crystal  is 
the  occurrence  of  the  prism  (/-2=210)  the  first  time  that  any  one  of 
the  vertical  prisms  has  been  ohserved  in  the  2d  tyj^e  of  either  humite 
or  chondrodite.  Tt  lies  in  botli  the  zones  e-(201),  /^^  (2^1),  and  e2(22i), 
«-  (22l)  which  answers  sufficiently  to  determine  what  it  is;  and  the  result 
thus  obtained  is  fully  sustained  by  good  measurements,  as  will  be 
seen  in  the  table.  This  plane  is  distinctly  present  on  one  side  only 
of  jB/  on  the  other  side  its  presence  is  barely  indicated.  Its  place 
here  is  taken  by  a  well  polished  and  conspicuous  plane  *,  which  is 
another  striking  instance  of  the  peculiar  nature  of  this  species  ;  its 
position  is  indicated  in  the  sphere  of  projection,*  and  the  angles  on 
e^  are  given  in  the  table.  The  index  was  calculated  for  each  pair  of 
measurements  38°  14',  39°  24  and  4'^  31,  6°  31  (see  in  the  table),  and 
the  results  obtained  were  identical.  From  the  first  pair  of  measured 
angles  'i  a.B  was  found  to  be  34°  30^'  and  from  the  second  *  a-S= 
34°  31'  (required  34°  32'  38").  The  index  obtained  was  60-f^  or 
60-38-1,  and  abnormal  as  it   certainly  is,  it  expresses  the  exact  posi- 

*  In  the  projection  *  is  placed  incorrectly  in  the  negative  quadrants ;  it  should  be  in 
the  positive  with  +  a,  +  n^,  +  r,  etc. 


86    E.  S.  Da7ia — Chondrodite  front  the  Tilly- Foster  Iron  Mine. 

tion  of  the  plane.  It  will  be  noticed  that  the  four  planes  upon  which 
the  inclination  of  *  was  measured  are  so  situated,  that  any  variation 
from  the  true  position  in  the  index  would  sliow  itself  very  conspicu- 
ously.    The  fundamental  angles  for  *  are  as  follows  : 

*/s^l(001)=  88°  51'  41'' 
^^^(lOO)^:  34     32    38 
*/s  (7(010)r=  55    28    49 

In  figure  16  a  crystal,  or  portion  of  one,  is  exhibited  which  is  holo- 
hedral.  It  is  irregular  in  this  respect,  however,  that  r^  forms  a  re- 
entrant angle  with  r^.  This  is  not  a  point  of  special  importance,  as  an 
irregularity  such  as  this  is  often  observed ;  but,  in  view  of  the  crystal 
which  has  just  been  described,  it  is  possible  that  here  also  there  has 
been  a  semi-revolution  parallel  to  the  basal  plane.  A  more  interest- 
ing crystal,  already  once  alluded  to,  is  shown  in  fig.  4.  It  is  con- 
spicuously hemimorphic,  as  far  as  the  form  goes.  It  is  large,  and 
admits  only  of  approximate  measurements,  but  there  is  no  doubt  but 
that  the  planes  as  given  have  been  determined  correctly.  In  view  of 
the  fact  that  a  revolution  parallel  to  0  would  produce  just  the  eifect 
we  have  liere,  and  as  such  a  twinning  law  has  been  shown  to  exist  in 
another  conspicuous  case,  it  is  altogether  probable  that  this  forms  an 
ample  explanation  of  what  is  observed.  Another  exactly  parallel 
case  is  noted  under  the  description  of  two  crystals  of  the  3d  type. 
The  above  described  crystal  was  somewhat  altei-ed,  and  so  far  imbedded 
in  the  matrix  that  any  experiments  as  to  its  pyro-electrical  character 
were  out  of  the  question. 

Chemical  composition. — I  am  glad  to  be  able  to  add  here  the  re- 
sults of  a  chemical  examination  of  the  chondrodite  of  the  2d  type 
from  this  locality,  by  Mr.  G.  \¥.  Hawes  of  the  Sheffield  Scientific 
School.  It  obviously  increases  much  the  value  of  this  memoir.  An 
analysis  by  Mr.  Breidenbaugh  has  already  been  quoted  (p.  3). 

The  material  analyzed  by  Mr.  Hawes  consisted  of  fragments  of 
crystals  of  the  2d  type,  selected  with  great  care  to  avoid  the  pres- 
ence of  any  altered  material.  It  had  a  deep  garnet-red  color  and  a 
brilliant  vitreous  luster.     Its  specific  gravity  as  determined  by  Mr. 

Hawes  was  3-22. 

Analysis  I.  Analysis  II. 

Silica  34-10  34-05 

Magnesia  53*17  53-72 

Ferrous  oxide  7-17  7-28 

Alumina  -48  "41 

Fluoi-ine  4-14  3-88 

99-06  99-34 


E.  S.  JDana—Chondroditefrom  the  Tilly-Foster  Iron  3fine.    87 

Following-  the  view  of  Kammelsberg,  that  the  higher  values  of  each 
constituent  are  nearest  to  the  truth,  Mr.  Hawes's  analysis  becomes  as 
follows.  For  comparison  the  results  obtained  by  vom  Rath  for  2cl 
type  crystals  from  Vesuvius  and  from  Sweden  are  added. 

Chondrodite. 
Brewster,  N.  Y.,  Hawes.         Swed 
Silica  34-10 

.  Magnesia  53-72 

Ferrous  oxide  7 '2 8 

Alumina  0-48 

Fhiorine  4-14 


99-72 


Silicon  15-91 

Magnesium  32-23 

Iron  5-66 

Aluminum  0-26 

Fluorine  4-14 

Oxygen  39*78 


HUMITE. 

V.  Rath. 

Vesuvius 

,  V.  Rath. 

33-96 

34-02 

53-51 

59-23 

6-83 

1-78 

0-72 

0-99 

4-24 

2-74 

99-26 

98-76 

15-85 

15-88 

32-11 

35-54 

5-31 

1-38 

0-38 

0-53 

4-24 

2-74 

39-58 

41-54 

97-98  97-47  97-61 

Transforming  the  iron  into  an  equivalent  of  magnesium,  as  also  the 
alumina  (2Al=:3Mg),  Mr.  Hawes  obtains  further: 

Silicon  15-91,  Magnesium  35-00,  Fluorine  4-14,  Oxygen  39-78, 

From  these  values  a  formula  is  deduced,  which  is  essentially  that 
of  the  Swedish  mineral  according  to  v.  Rath,  20(Mg  Si20g)+ 
MggSigFl^g.  The  close  correspondence  between  the  three  analyses 
in  the  above  table  is  certainly  very  remarkable.  It  would  have  been 
extremely  interesting  to  have  added  an  analysis  also  of  crystals  of 
the  1st  and  3d  types;  but,  as  will  be  appai-ent  from  what  follows,  the 
material  was  not  to  be  obtained. 

In  completing  the  description  of  this  variety  of  the  mineral,  in 
general  it  may  be  repeated  that  it  occurs  usually  in  narrow  veins,  and 
when  free  from  alteration  has  iiniformly  a  deep  garnet-red  color.  A 
cleavage  such  as  exists  in  humite  (parallel  to  the  basal  plane)  and  has 
been  observed  by  Kokscharow  on  chondrodite  from  Pargas,  could  in 
no  case  be  discovered.  The  fracture  is  always  conchoidal,  and  the 
only  thing  that  suggested  cleavage  was  the  laminated  structure  of 
the  massive  specimens  described,  and  the  fractures  parallel  to  e^ 
which  were  quite  conspicuous  on  two  or  three  specimens.  The  ma- 
terial in   hand  Avas   not    well   adapted   for   optical   determinations- 


88    E.  tS.  Dana — Chondrodite  from  the  Tilly-Foster  Iro7%  Mine. 

but  some  interest  in  <>•  results  liave  been  obtained  whicli  are  described 
in  the  closing  pages  of  this  paper. 


2.  Description  of  (Jri/stals  of  Type  III. 

Since  it  was  shown  by  Kokscharow  that  the  Pargas  chondrodite 
was  identical  with  the  second  tyjie  of  humite,  it  was  natural  to  ex- 
pect that  further  investigation  would  prove  the  existence  also  of  the 
two  remaining  types.  Up  to  the  present  time  that  expectation  has 
been  unfulfilled,  and  it  has  been  reserved  for  the  Brewster  locality  to 
give  this  confirmation  of  Scacchi's  interesting  discovery.  The  crystals 
of  the  3d  type  are  exceedingly  rare,  three  or  four  specimens  being  all 
that  have  thus  far  been  foiind,  and  from  these  only  two  individual 
crystals  could  be  obtained  which  allowed  of  measurement.  Fortu- 
nately these  two  crystals  are  very  satisfactory,  bemg  small  and  bril- 
liant, and  establish  the  fact  as  well  as  a  hundred  could  do.  Figures  11 
and  12  show  one  of  the  crystals,  and  figure  13  the  other.  The  appear- 
ance of  the  first  crystal  is  best  shown  in  the  second  of  these  figures. 
As  will  be  seen,  the  planes  are  the  same  as  in  humite,  and  they  are  for 
the  most  part  hemihedral  and  situated  in  the  same  way  ;  i.e.,  they  in- 
clude+p',+p', +//,  and  -p\-~p\—fj\  ^\\(\.—v\-y\-v\—v'  as 
also  1^,1^,1*.  Ill  the  n{v)  series  the  planes  are  distinct  in  the  negative 
half,  but  the  crystal  is  incomjjlete,  and  it  is  a  little  uncertain  whether 
the  -|-  series  should  not  in  part  be  added  in  the  symmetrical  drawing 
fig.  11;  on  humite.  III,  these  planes  are  both  positive  and  negative. 
No  brachydomes  are  visible,  the  edge  being  rounded  and  rough.  ni~ 
of  Scacchi  may  also  be  present,  but  that  is  a  little  doubtful. 

The  second  crystal  is  of  very  different  form,  and  Avhile  the  first  was 
affixed  to  the  rock  so  that  only  one-half  was  developed,  this  one  was 
imbedded  in  bnicite,  and  entirely  free  in  it.  It  was  perfectly  formed 
on  all  sides,  being  almost  as  perfect  as  the  projected  drawing,  with  the 
exception,  however,  of  the  acute  (brachydiagonal)  edge,  which  was 
mostly  broken.  When  only  the  upper  part  of  the  crystal  is  considered, 
it  will  be  seen  that  the  hemihedrism  is  like  that  in  the  other  case,  ex- 
cept that  (f  is  holohedral.  For  macrodomes  there  are  /'(f-7^023), 
z-(l-73=011),  /'(2-7— 021),  /'(4-7=:041);  the  last  has  not  been  observed 
on  humite.  On  measuring  the  planes  below  it  was  found  that  they 
were  not  distributed  as  was  expected  in  accordance  with  the  mono- 
clinic  character  of  the  crystal ;  instead,  either  exti-emity  of  the  brachy- 
diagonal axis  was  diffei'ently  developed.  This  is  clear  in  the  figure,  it 
being  but  a  more  complicated  repetition  of  what  was  observed  in  one 


jE  ^S,  Dana — Chondrodite  from  the  Tilly-Foster  Iron  Jline.     89 


of  the  very  simple  crystals  of  the  2d  type  (see  fig.  4  and  page  18). 
There  are  present  also  at  one  extremity  it  ^'(t"^^^'^^''^)?  though  the  plane 
could  only  be  approximately  measured.  This  is  probably  also  to  be 
explained  as  having  resulted  from  a  revolution  parallel  to  the  basal 
plane.  The  crystal  was  very  small  and  not  at  all  adapted  to  expei*i- 
mcnts  having  in  view  the  discovery  of  any  proper  hemimorphic 
developiuent.  The  angles  measured  on  both  these  crystals  are  con- 
tained in  the  following  tables. 

Table  XII. 


Chondrodite. 

Hiunite. 

Calc. 

^=0(001). 

Meas  (XX).  Meas  (XXI) 



V.  Eath. 
Calculated. 

£ 

4 

407 

143°  20' 

9" 

143° 

11'  29" 

C^ 

4-1 

041 

100   1 

7 

l^ 

2-1 

021 

109  27 

35 

109 

27  54 

I- 

l-l 

Oil 

125  14 

49 

125 

15  18 

il 

2 

— -i 
3 

023 

136  40 

4 

136 

40  34 

P' 

A-2 
11 

2811 

131  25 

57 

131'  46' 

131° 

24' 

131 

24  49 

P" 

1-^ 

289 

125  50 

6 

j  125  37 
I  125  47 

125 

48 

125 

49   0 

p= 

1-^- 

287 

119  19 

18 

j  119  35 
]  119  15 

118 

36 

119 

18  19 

P' 

1-2 
5 

285 

111  51 

38 

j  111  44 
(111  49 

112 

0 

111 

50  50 

P' 

8  _ 

283 

103  32 

4 

103  41 

103 

38 

103 

31  33 

p« 

8-2 

281 

94  35 

15 

j  94  31 
I    94  13 

94 

48 

94 

35   4 

v' 

4 

T 

447 

132  17 

48 

132 

16 

132 

16  43 

V^ 

4 
~5 

445 

123   1 

8 

122 

32 

123 

0   8 

^3 

4 

443 

111  18 

7 

111 

5 

111 

17  23 

V^ 

4 

441 

97  24 

20 

97 

29 

97 

24   3 

Unfortunately  the  inclination  to  C  on  no  one  of  the  pyramidal  planes 
could  be  measured  with  perfect  accuracy ;  the  measurements  are  good, 
yet  not  entirely  trustworthy.  These  planes,  though  brilliant,  are  uni- 
formly fi-actured  in  the  manner  already  explained,  and  this  made  all 

Tbans.  Conn.  Acad.,  Vol.  III.  12  July,  1875. 


90    E.  S.  Dana — Chondrodite  from  the  Tilly-Foster  Iron  Mine. 


Taijle  XIII. 
Chondrodite. 


Calc. 

C=i-l  (010). 
Meas  (XX).  Meas  (XXI) 

i* 

4-1 

041 

169° 

58' 

53" 

170°   2' 

(? 

2-1 

021 

160 

32 

25 

160  36 

i^ 

1-1 

Oil 

144 

45 

11 

144  47 

«! 

2 

023 

133 

19 

56 

133  (ap.) 

p« 

n-^ 

2811 

132 

56 

12 

j  133  13 
I   132  38 

132°  46' 

P' 

1-9 

9 

289 

137 

26 

13 

j  137  36 
1  137  27 

137  21 

P" 

f^ 

287 

142 

22 

50 

j  ]42  35 
1  142  20 

142  38 

P' 

1-^ 

285 

147 

28 

24 

147  26 

P' 

1.-2 
3 

283 

152 

1 

44 

152   2 

P' 

8-2 

281 

154 

53 

20 

155   0 

154  58 

v' 

4 

y 

447 

123 

31 

12 

v' 

4 

445 

128 

5 

52 

V^ 

4 
"3 

443 

133 

16 

51 

133  57 

V* 

4 

441 

136 

51 

' 

136  42 

these  angles  a  little  uncertain.  The  macrodomes  in  one  case  gave 
good  measurements;  and  making  use  of  the  best  of  them,  C/\i^{l-i) 
r=144°  47',  and  also  the  same  prism  as  in  type  II,  after  the  analogy 
of  humite,  the  angles  were  calculated  throughout.  It  was  found, 
however,  that  wherever  trustworthy  they  corresponded  so  closely  to 
what  was  required  to  satisfy  the  ratio  of  10:9  for  the  vertical  axes 
(asserted  as  approximately  true  by  Scacchi,  i.  e.,  5  :  9  for  his  axes,  and 
finally  proved  rigidly  by  vom  Ratli),  that  the  calculations  were  made 
on  this  supposition.  The  calculated  angles,  as  now  given,  conse- 
quently have  as  their  basis  the  prismatic  angle  Iy,,I=z94°  44'  14"  and 
the  macrodome  angle  C^i'=l^-i°  45'  11  ". 
The  coiTcsponding  parameters  are  : 

a  (vert.)  =  1-41512;  b  =  I  ;  c  =  TOSBSO. 


E.  JS.  Dana — Chondrodite  from  the  Tilly-Foster  Iron  Mine.     91 

Very  little  further  can  be  said  in  regard  to  the  crystals  of  tlie  3d 
type.  Those  observed  had  a  somewhat  diiferent  color  from  those  of 
type  II ;  that  is,  the  color  was  more  yellowish,  less  of  a  pure  garnet- 
led — though  this  may  be  accidental.  No  analysis  was  possible  of 
coui'se;  and  even  the  sjjecitic  gravity  was  out  of  the  question  also,  for 
the  one  loose  crystal,  in  addition  to  its  small  size,  had  imbedded  in 
it  a  still  smaller  crystal  of  ripidolitc,  making  any  gravity  determina- 
tions obviously  uurelial)Ie. 

The  method  of  occurrence  was  much  like  that  of  the  brilliant  crys- 
tals of  the  second  type  ;  that  is,  they  w^ere  found  implanted  on  the 
massive  rock  adjoining  small  veins.  The  associated  minerals  Avere 
magnetite,  ripidolite  in  clear  transparent  crystals,  and,  probably  as  a 
later  formation,  brucite. 

3.  Description  of  Crystals  of  Type  I. 
The  occurrence  of  large,  coarse  crystals  of  quite  impure  chon- 
drodite,  imbedded  in  the  massive  material,  has  already  been  de- 
scribed ;  these  belong,  at  least  in  part,  to  the  first  of  Scacchi's 
types.  As  has  been  remarked,  the  crystals  of  this  character  do 
not  often  admit  of  exact  determination,  but  in  two  cases  they 
were  so  good  as  to  allow  of  their  crystallographic  relations  being 
accurately  made  out.  The  accompanying  wood-cuts,  figui'es  22 
and   23,  give  faithful  representations  of  their  appearance  and  size. 


RU 


«^ 

J^l 

R2\ 

/     R3 

/r 

R^       \ 

*L__b4 

J 

R^         \ 

— -— ^-,^_^ 

1 

r. 

^^=Sh 

1 

,4 

^^z^ 

R^ 


R^" 


Fig.  22.  Fig.  23. 

It  will  be  seen  that  they  are  both  quite  imperfect,  and  it  was  on  this 
account  that  no  attempt  was  made  to  make  a  symmetrical  drawing 
of  either  of  them.  In  each  case  the  crystals  w^ere  so  distorted  as  to 
give  a  sharp  edge  between  the  diagonally  situated  pyramidal  planes; 
this  furnished  an  opportunity  for  relial)le  measurements.     The  plant's 


92    JiJ.  8.  Dana — Chondrodite  from  the  Tilly-Foster  Iron  Mine. 

were,  of  course,  destitute  of  all  luster,  but  they  were  mostly  smooth 
and  large  enough  to  allow  of  the  convenient  use  of  the  hand  gonio- 
meter. 

R"^  on  7^"  (behind)  gave  measurements  varying,  in  a  series  of  trials, 
from  78°  to  79",  required  79°  4'. 

7t"  on  R'  (behind)  gave  62^,  required  63°  l'. 
i?"  on  R^  (l)ehind)  gave  72  ,  required  71  174- 
Zil'  on  R"  (behind)  gave  72    ,  required  71    17^. 

These  angles  on  both  crystals  were  identical  within  the  allowed 
error  of  observation  (say  30').  The  above  are  the  best  angles 
afforded  by  any  of  the  planes. 

It  is  entirely  impossible  to  refer  these  angles  to  any  of  the  forms  of 
the  second  type.  When  compared  with  the  third  type,  it  is  seen 
that  on  making  the  supposition  that  R'  and  W  (front)  are  p^  and  p* 
respectively,  and  R"^  and  R^  (behind)  are  p*  and  p^,  we  obtain  for: 

p\\  p'  (behind)=77°  12';    pV  p'  (behind)~65'^  6'; 
p'^  p'  (behind)=:70°  32';  pV  p'  (behind)=:7l°  37'. 

It  will  be  seen,  by  comparing  these  with  the  ])reviously  given  angles, 
that  the  measured  angles  correspond  much  better  with  the  iirst  type, 
and  my  confidence  in  them  is  so  great  that  this  would  alone  be  re- 
garded as  sufficient  to  establish  the  point ;  and  that,  without  refer- 
ence to  the  fact  that  tlie  supposed  method  of  occurrence  of  the  third 
tyj^e  planes  is  contrary  to  all  the  laws  of  the  species. 

The  decisive  proof  is  derived  froTU  the  fact  that  both  crystals  are 
certainly  holohedral,  the  planes  on  both  sides  being  similar  with  the 
exception  of  R\  and  there  is  nothing  of  the  obliquity  which  is  ob- 
served in  the  hemihedral  forms. 

The  measured   angles  of   C  on  _Z?\  right  and  left,  were  identical, 

though  not  obtainable  with  exactness  ;  the  measurements  gave  152^° 

-154°  :  this  is  also  true  for  C  on  R\  right  and  left,=  140i°-142^°. 

3 

In  the  first  crystal  e/'::^ i    (035)   occurs,   and    in    the    other    J'^ 

o 

(l-7=r01 1).  The  occurrence  of  C  is  also  to  be  noticed,  as  it  is  rare  on 
humite;  in  fig.  23,  the  oscillatory  combination  of  7^"*  and  R"  will  be 
also  observed. 

The  following  table  includes  the  most  important  angles  for  the  oc- 
curring })lanes,  calculated  from  the  fundamental  form  of  the  second 
type  on  the  assumption  that  the  lateral  axes  are  equal,  and  the  vertical 
axes  have  the  ratio  of  14  :  15.  The  measured  angles  are  also  added 
thouo"h  only  approximate ;  in  the  form  given  they  were  obtained  imme- 
diately from  the  measurements  over  the  top  of  the  crystals  (see  above). 


E.  S.  Dana— (Jhondroditc  from  the  Tilly-Foster  Iron  Mine.     93 


Tahmc  XIV. 
Chondrodite. 


Humite. 


C=M(010). 
Calculated. 

.1=  0 
Mens. 

(001). 
Calc. 

V.  Ratli. 
Calculated. 

J« 

l-l 

Oil 

145°  43'  44" 

124° 

16'  16" 

124" 

16'  45" 

J> 

3 

035 

138 

38  38 

R' 

f^ 

3-6-10 

129  12  5*7 

135° 

135 

53  35 

135 

52  23 

B? 

Q 

4-^ 

368 

134  28  38 

129i 

129 

32   3 

129 

30  52 

W 

1-2 

122 

140  30  10 

121i 

121 

45  28 

121 

44  23 

R* 

1-^ 

364 

147   6  34 

112 

25  28 

112 

24  37 

R5 

3-2 

362 

152  49  49 

101 

101 

39  30 

101 

39   2 

The  two  crystals  described  are  the  only  ones  which  could  be  posi- 
tively identified.  It  is  very  probable,  however,  that  of  those  found 
others  also  belong  here,  as  they  have  much  the  same  appearance  and 
habit.  These  crystals  are  all  considerably  altered,  being  generally 
soft  enough  to  be  cut  with  a  knife,  and  for  this  reason  a  chemical 
analysis  would  be  of  little  value.  The  color  of  the  crystals  is  gray  to 
grayish-yelloM',  and  the  material  of  which  they  are  composed  is  never 
pure,  and  often  quite  heterogeneous.  In  this  respect  they  recall  the 
bi'own  crystals  described  by  v.  Rath  as  occurring  at  Nya-Koppar- 
berg. 

Whether  brilliant  crystals  of  the  first  tyjje  exist,  as  they  do  of  the 
other  types,  must  be  left  for  the  present  undecided. 

4.    On  the  Optical  Properties  of  Chondrodite. 

In  the  preceding  pages  the  question  of  the  orthorhombic  or  clino- 
rhombic  crystallization  of  the  chondrodite  has  not  been  discussed.  In 
fact,  nothing  was  detected  by  the  measurements  sustaining  any  other 
conclusion  than  that  of  Scacchi  and  vom  Rath,  that  the  crystals  were 
fundamentally  orthometric.  Still  the  hemihedral  character  of  the 
second  and  third  types  seem  to  point  to  a  clinometric  form,  and  this 
is  apparently  supported  by  the  optical  characters  obtained.  The  ma- 
terial available  for  optical  investigations  was  very  scanty,  and,  with 
the  exception  of  one  crystal,  poorly  adapted  for  the  purpose. 

The  crystal  referred  to  was,  properly,  but  the  fragment  of 
what  was   originally  a  specimen  of  considerable   size    and   beauty ; 


94    E.  S.  Dana— Chondrodite  from  the  TUhj-Foster  Iron  Mine. 

when  unbroken  it  must  have  been  nearly  an  inch  in  length.  In  the 
condition  in  which  it  was  found  it  showed  only  the  brachydomes  e' 
ande^,  with  the  pyramids  ?^^,  n^,  and  m^  ;  it  had  the  deep  garnet-red 
color  of  crystals  of  the  second  type,  and  with  the  exception  of  the  uni- 
versally i^resent  fractures  was  perfectly  clear  and  transparent. 

On  the  optical  jDroperties  of  the  mineral  hi  question,  we  have,  as 
far  as  I  have  been  able  to  find,  no  information  except  what  has  been 
giveu  by  DesCloizeaux,  Manuel  de  Mineralogie,  1862,  p.  141.  He 
says  :  "  Double  refraction  energetic  ;  positive  bisectrix  normal  to  ^  *  ; 
optic-axes  situated  in  the  jdane  parallel  to  the  base ;  divergence  in 
oil    for   red   and  yellow   rays,  82°  14'.     Dispersion  almost  nothing; 

Guided  by  the  above,  a  section  was  cut  from  the  crystal  described, 
which  was  pai-allel  to  C',  i.  e.,  perpendicular  to  the  brachydomes  pres- 
ent. The  examination  of  this  section  showed  :  i  st,  that  the  acute 
bisectrix  is  normal  to  G  (i-i,  010)  ;  2d,  that  this  bisectrix  is  positive  ; 
3d,  that  the  optic-axial  angle  is  large,  the  axes  being  seen  only  when 
oil  is  used  ;  but  4th,  that  the  axes  do  not  lie  in  the  hasal  jjlane,  but  in 
a  plane  making  an  angle  of  about  15  t°  with  it.  This  last  point  was 
so  unexpected  and  anomalous  that  every  effort  was  made  to  explain 
the  measiirements  in  soine  other  way,  but  with  no  success.  The 
planes  on  the  crystal  had  been  carefully  measured,  before  the  slicing, 
and  the  angles  agi-eed  perfectly  with  those  of  type  II  for  the  planes 
mentioned,  so  that  it  was  impossible  to  assume  that  the  crystal  had 
not  been  correctly  put  into  position.  By  means  of  a  staiiroscope, 
made  by  Fuess  in  Berlin,  after  the  excellent  pattern  of  Groth,*  the  posi- 
tion of  the  two  axes  of  polarization,  as  referred  to  e^,  and  also  to  e^  in 
plane  C,  were  carefully  determined.  The  measurements  were  repeated 
twenty  times,  the  error  arising  from  an  imperfect  adjustment  of  the 
Nicols  being  eliminated  in  the  usual  mannei*.  The  result  was  as 
follows : 

Supplement  angle  made  by  the  plane  of  the  axes — 

with  e^(|-^=r203),  18°  9' ;  hence  with  the  basal  plane,  (J,  25"  50'. 
withe^(2-^=201),  45°  9';       "  "  «  "      25°  46'. 

In  order  to  confirm  these  results,  other  crystals  were  sought,  which 
would  admit  of  like  determinations.  None  could  be  found  which 
would  serve  for  measm-ing  the  axial  angle ;  but  two  small  ones,  on 
which  the  plane  C  was  naturally  developed,  proved  to  be  clear 
enough  to  allow  of  measurements  with  the  stauroscope.     The  first 

*See  Pogg.  Ann.,  cxliv,  34,  1870. 


K  S.  Damt — Chan  drodite  from,  the  TilU/-Fostei'  Iron  Mine.    95 

nloiie  gave  accurate  results;  on  it  tlie  angle  of  the  same  plane  with 
6"(|-?=i206)  was  deterniined  with  equal  care.     The  results  were : 
4°  55'  for  the  angle  with  ea;  and  hence  25°  59'  with  G. 

The  agreement  with  the  angles  given  above  is  as  close  as  could  be 
desired.  In  the  other  case,  the  rather  rare  plane  B  (^-^r=100)  was  pres- 
ent ;  the  crystal  was  minute,  however,  and  the  determination  only 
approximate.  It  was  found  that  the  normal  to  the  axial  plane  made 
with  B  an  angle  of  65°-V0°,  and  hence  with  the  normal  to  the  basal 
plane  20°-25°. 

With  so  ample  confirmation  the  point  made  cannot  be  even  ques- 
tioned, and  it  remains  to  reconcile  it  with  the  crystallographic  proper- 
ties of  the  species.  It  will  be  seen  at  once  that  the  position  of  the  optic 
axes  is  totally  at  variance  with  the  accepted  orthorhombic  character 
of  the  crystals ;  but  it  conforms  to  the  rule  for  monoclinic  crystals,  as 
one  axis  of  polarization  is  normal  to  the  plane  of  symmetry  C,  and 
the  others  lie  in  it,  or  in  other  words,  the  optic-axes  lie  in  a  plane  per- 
pendicular to  the  axis  of  symmetry.  The  angles  measured  and  cal- 
culated, given  in  the  various  tables,  show  that  the  variation  from  the 
rectangular  type,  if  it  really  exist,  must  be  very  slight,  as  the  agree- 
ment between  the  angles  measured  and  those  calculated  on  the 
assumed  prismatic  basis  is  very  close — it  being  remarked  that  some  con- 
siderable variations  in  the  angles  given  in  the  tables  are  amply  ex- 
plained by  the  imperfection  of  the  crystals.  Note  the  angles  measured 
for  m^/\m^  on  the  twin  crystal  described  on  page  18.  It  was  not  to 
be  expected  that  the  variation  in  the  optical  character  of  the  crystals 
would  be  so  decided  in  view  of  the  slight  divergence  which  is  possi- 
ble in  the  crystalline  form.  I  reserve  for  the  future  the  careful  re- 
vision of  the  angles  of  this  species,  when  I  shall  hope  to  be  able  to 
command  a  more  abundant  supply  of  satisfactory  material.  It  may 
be  added  that  the  hemihedral  character  of  the  second  and  third  types 
of  humite  long  ago  suggested  the  idea  that  they  were  oblique  inform  ; 
but  all  the  crystallographic  investigations  thus  far  have  seemed  to 
deny  this.  In  the  Mineralogy  of  Brook  and  Miller,  the  form  is  made 
oblique,  but  this  seems  to  be  due  to  a  misunderstanding  of  the  planes 
occurring  on  the  crystals. 

It  would  have  been  interesting  to  extend  these  observations  to  the 
two  remaining  types,  but  the  material  did  not  allow  of  it.  It  was 
also  desired  to  investigate  the  same  subject  for  humite,  but,  though 
some  good  specimens  are  to  be  found  in  the  Yale  cabinet,  there  were 
no  satisfactory  crystals  to  be  had,  and  the  matter  is  left  for  others, 
who  have  a  larger  choice  of  specimens.  The  axes  as  already  men- 
tioned do  not  appear  distinctly  except  in  oil ;   in  the  first-mentioned 


96 


E.  S.  Dana — Ghondrodite  from  the  Tilly-Foster  Iron  Mine. 


section  they  admitted  of  good  measurements.     The   mean  of   thirty 
determinations  of  the  angle  for  red  rays  gave — 

2Ht>'=88°  48' :  the  extremes  being  88**  36'  and  89°  O'. 

With  a  yeHow  light  (sodium)  the  angle  was  essentially  the  same, 
but  tlie  mean  was  10'  or  15'  smaller,  which  would  indicate  that  the 
dispersion  is  /3]>?^,  but  the  matter  cannot  be  considered  to  be  beyond 
doubt.  No  other  dispersion  was  observed,  that  is,  none  parallel  or 
perjDcndicular  to  the  plane  of  polarization. 

The  index  of  refraction  of  the  oil  employed,  as  determined  by  Pro- 
fessor Wright  and  myself,  was  1"466. 

In  conclusion,  I  have  to  expi-ess  my  very  great  obligations  to  Prof. 
Allen  for  his  kindness  in  giving  me  free  use  of  all  the  specimens  in 
his  valuable  cabinet.  Both  of  the  crystals  of  the  third  type,  as  well 
as  several  others  mentioned,  came  from  his  collection  ;  in  fact  it  was 
Prof.  Allen  who  first  made  known  the  special  interest  connected  with 
the 'locality.  To  Mr.  Cosgriff,  the  superintendent  of  the  Tilly- 
Foster  Iron  Mine,  I  am  also  much  indebted  for  his  uniform  kind- 
ness and  courtesy  to  me  at  the  several  occasions  when  I  have 
visited  the  mine  ;  as  also  for  the  gift  of  several  fine  specimens. 


IV. — Ox  THE  Til. vxscEN  DENTAL  CiKVEs  s'mi/ smmy=asu\XHiunx-\-b. 
With  Plates  XIV— XXXVII.  By  II.  A.  Newton  and  A.  W. 
Phillips. 

1.  Algebraic  curves  have  been  studied  hitherto  more  than  trans- 
ceudeutal.  A  few  of  tlie  latter  have  beeu  giveu  in  the  text  books, 
but  attempts  to  classify  the  numerous  varieties  of  transcendental 
curves  have  been  rare. 

From  the  form  of  a  transcendental  curve  it  is  not  easy  to  state  an 
equation  that  can  represent  it.  The  simpler  inverse  problem  of 
describing  the  curve  from  the  equation  is  naturally  the  first  to  be 
undertaken.  The  forms  that  result  may,  when  compared,  suggest  the 
solution  of  the  direct  problem.  We  have  thought  it  worth  while, 
therefore,  to  select  for  study  a  single  one  of  the  numberless  transcen- 
dental equations,  and  to  exhibit  a  few  of  the  very  many  plane  curves 
which  that  one  equation  furnishes.     1  he  equation  selected  is, 

sin  y  sin  my  =l  asinx  sin  nx-{-b,  ( 1 ) 

in  which  there  are  four  arbitrary  constants  a,  b,  m,  and  n,  with  two 
coordinates,  x  and  y. 

2.  We  assume  that   ui   and   u  are  each  less  than  unity.     If  either, 

for  example  >;/,  is  greater  than  unity,  we  may  change  the  unit  for  y 

in  the  ratio  of  1  :m\)j  writing  y'=:zmy.     The  first  member  of  Eq.  (l) 

.     1      ,  .  .  ,    ,  .     1 

then  becomes   siny'  sin  —  y',  where  the  coefficient  of  y  is  — ,  which  is 

less  than  unity. 

In  the  equation  thus  changed,  we  have  assumed  in  our  figures  the 
units  for  x  and  y  equal,  and  the  axes  rectangular.  The  effect  of  a 
different  supposition  in  either  particular  can  be  readily  understood. 

3.  Curves   xchose  equations   <ire  y=zasi)ixsinmx.     It   was   found 

convenient  to  draw  several  auxiliary  curves   whose  equations  are  of 

the  form, 

y=zaii\\\x^mnix.  (2) 

A  convenient  arlutrary  value  being  assumed  for  a,  to  m  was  given  in 
turn  all  the  values  of  the  proper  fractions,  which,  reduced  to  their 
lowest  terms,  have  denominators  less  than  12.  The  forms  of  these 
curves  are  shown  on  plates  XIV  and  XV,  excepting  a  few  in  which 
m  has  11  for  denominator.  In  fig.  37  is  shown  the  beginning  of  the 
curve  when  m  has  the  irrational  value  s/\.  The  axis  of  x  is  drawn 
Trans.  Conn.  Acad.,  Vol.  III.  13  August,  1875. 


98         Neioton,  and  Phillips  on  certain  Transcendental  Curves. 

in   the  figures.     The  origin  is  the  point   at  the  left  of  each  figure 
where  the  curve  touches  the  axis  of  x. 

P  p' 

It  will  be  convenient  at  times  to  put  m=  — ,  and  nz=z  —,  where/?, ^, 

p',  and  r/,  are  integers,  and  the  fractions  are  reduced  to  their  lowest 
terms. 

4.  Properties  of  the  curves  of  Eq.  (2).  By  inspection  of  the  curves 
on  plates  XIV  and  XV,  and  of  their  equations,  we  readily  deduce  the 
following  properties  : 

a.  The  value  of  y  is  not  greater  than  a. 

h.   When  either  x  or  inx  is  a  multiple  of  ;r,  ;y=:0. 

c.  There  are  maxima  or  minima  values  of  //  when  wi  tan  ,r=  —  tan  ma*. 

(/.   When  ni  is  rational   the   values  of  y  repeat ;  after  qn  if  p  and  q 

are  both  odd ;  after  'Iqn  if  either^:)  or  q  is  even. 
e.   When  m  is  irrational  the  curve  does  not  repeat  its  form. 
/'.  The  curve  is  symmetrical  about  the  axis  of  y,  and  about  an  axis 

through  the  middle  point  of  each  cycle. 
g.  If  p  or  q  is  even.,  the  curve  is  symmetrical  about  the  point  y=0, 

qn 

^' 
h.  There  are,  in  each  distance  -Iq-n:  along  ,<■,  p-\-q  maxima,  and  an 

equal  number  of  minima  values  of  y. 

5.  The  value  of  y  in  Eq.  (2)  may  be  regarded  as  made  up  of  two 

a  a 

parts,   since   y=La&mx  %\nnix=z~  go^[\  ~m)x — — cos(l-|-m)a.'.         In 

fig.  22,  where  mz=L^,  these  parts  are  sej^arately  shown.     The  continu- 

a 
ous  line   represents  the  curve  yz=:  —  qo^[\—^)j\     having    one     com- 

])lete  oscillation  in   a  distance  of   IQn  along  ii-.     By  laying  ofl" below 

and  above  this  curve  the  second   part  of  y,  that  is— —  cos(l -|-f)^, 
we  have  the  curve  y=.a%mx  sinf.«. 

6.  Use  of  the  auxiliary  curves,  Eq.  (2).  To  draw  the  curves  from 
equation  (1),  even  after  all  the  usual  devices  for  saA'ing  labor  have 
been  employed,  requires  the  frequent  solution  of  equations  of  the 
form  sin  a;  sin?;?  35:=  c.  This  equation  gives  a  set  of  values  of  x  for 
each  cycle  of  the  curve.  To  find  each  value  of  x  requires  a  solution 
l)y  trial  and  error,  a  very  simple  process,  but  when  often  repeated 
quite  tedious.  By  the  curves  figs.  1-37  carefully  traced  on  cross- 
section  paper  we  may  by  merely  running  the  eye  along  the  line  y=.c 


NeuitoH  and  PhUUpn  on  certain  IVanscendental  Curves.         00 

obtain  by  iiispoctit)ii  all  the  values  of  x  to  a  sutHcieiit  degree  oi" 
accuracy. 

7.  Equation  (1)  when  a=zb=zO.     The  ecjuatiou 

siny  sin  wymO,  ['A) 

consists  of  the  two  equations  sinyzrO,  and  sin  ?>iy=:0,  and  is  satisfied 
by  the  values  i/:=l7r,  and  i/ii/=f7r,  where  /  is  0,  or  any  integer.  In 
fig.  60  the  horizontal  lines  belong  to  the  equation  sin  //  sin  |-  ;y^=0.  They 
consist  of  two  series,  one  at  intervals  of  ;r,  the  other  at  intervals  of 
2^7r.  Tf  through  the  intersections  of  the  curve  in  fig.  25  with  the 
axis  of  .(•  there  be  drawn  lines  peri)endicular  to  that  axis,  the  lines  for 
smx  sin  |a*r=:0  would  be  obtained.  The  heavy  lines  of  fig.  60  I'epre- 
sent  double  lines,  corresponding  to  points  of  tangency  in  fig.  25. 

8.  Equation  (1)  ivhere  a=0.  The  equation  (1)  becomes  by  mak- 
ing a=0,  and  for  convenience  changing  the  axes, 

sina'sinwia-^J.  (4) 

This  does  not  contain  y,  and  therefore  represents  straight  lines 
parallel  to  the  axis  of  y.  If  the  straight  line  y=b  be  drawn  parallel 
to  the  axis  of  a^  to  cut  the  curve  y=s\nx  sminx,  and  through  the 
several  points  of  intersection  straight  lines  be  drawn  parallel  to  the 
axis  of  y,  these  lines  will  evidently  be  those  represented  by  the  equa- 
tion since  iimutxz=.b. 

In  fig.  60  the  vertical  lines  rei»resent  the  equation  sinx  sm^x:='f. 
If  the  curve  in  fig.  26  be  cut  by  a  line  parallel  to  the  axis  of  x  and 
distant  from  it  two-fifths  of  the  largest  ordinate,  the  intersections  will 
correspond  with  the  intersections  of  any  horizontal  line  in  fig.  66  by 
the  several  vertical  lines.* 

9.  Equation  (1)  iohere  a=\,  b=0,  m=zn—\.     The  equation 

sin  y  sin  ?/=sin  x  sin  x  (5) 

becomes  sin  y=  ±sin  .'■,  or  ;/z=Itt  ±:-'',  I  being  0,  or  an  integer.  The 
cvirve  consists  of  two  series  of  parallel  equidistant  straight  lines,  the 
one  parallel  to  //=.>',  the  other  to  y=-x,  and  both  cutting  the  axes 
at  intervals  of  rr.  The  locus  is  represented  in  fig.  38,  where  the  origin 
is  any  point  of  intersection. 

1 

10.  Equation  (1)  v^here  a=\,  b=0,  m.=n=  —  .      The  equation 

sin  y  sin— V— sina;  sin  —x  (6) 

q'  q 

is  one  of  the  simpler  examples  of  equation  (1). 


*  The  unit  of  abscissas  in  plates  XIV  and  XV  is  smaller  than  in  the  other  plates. 


100       Nev)ton  (Did  Phillips  on  certain  Tnuiscendental  Curves. 

a.  It  is  satisfied  if  y^=-'X.^  or  if  y-=.  — x.     Hence  the  two  straight  lines 

y=  zb'*'  form  part  of  the  locus  of  equation  (6). 
h.  If  'llqn-^x  l)e  put  for  cc,  /  being   an  integer,  the  equation  is  un 

changed,  whether  q  be  odd  or  even. 

c.  If  q  be  odd  the  equation  will  be  unchanged  if  lq7r-\-.i'  be  jnit  for  x. 

d.  The  curve  repeats  itself  to  the  right  and  left,  and  also  above  and 

below,  at  intervals  of  qn  \i  q  is  odd.,  and  at  intervals  of  Iqn 
if  q  is  even. 

e.  Straight  lines  parallel  to  yr=±./',  and  cu.tting  the  axes  at  intervals 

of  qrr,  or  2q7t,  according  as  q  is  odd  or  even,  belong  to  the 
locus  of  equation  (6). 

f.  These   straight  lines   divide  the   infinite  plane  of  coordinates  into 

equal  squares  for  a  given  value  of  q.  Each  square  contains  a 
similar  and  equal  portion  of  the  locus.  If  q  is  odd,  that  portion 
is  not  always  similarly  placed,  ibr  it  may  have  two  positions 
with  respect  to  an  axis. 

g.  If  q  is  even,  isolated  points   at   the  centers  of  the   squares  {f) 

belong  to  the  locus. 

h.  The  equation  (6)  is  satisfied  if  sin  ^=:0,  and  9my=.0.  Hence  the 
locus  of  (6)  passes  through  the  angular  points  of  all  the  squares 
formed  by  the  lines  sin  a;z=0,  and  sin  y^O  (Art.  V.) 

i.  A  few  curves  representing  equation  (6)  are  shown  in  figs.  40-4'?. 
The  axes  are  not  drawn.  Any  point  of  intersection  of  straight 
lines  that  is  sui'rounded  by  an  oval  may  he  taken  for  the  origin. 
The  several  propositions  of  this  article  will  be  more  easily  un- 
derstood by  inspection  of  the  curves. 

11,  Equation  (1)  lolien  a=l,  bz=0,  ni=:n:=  /-  .     In    this   case   the 

equation  becomes, 

smy8iu±--y=:iiinx't^m^.x.  (7) 

q'  q 

The  properties  of  the  curves  of  equation  (7)  are  in  many  respects  like 

those  of  equation  (tj). 

a.  The  two  straight  lines  y:=:  ±cc  belong  to  the  locus. 

b.  If  p  and  q  are  both  odd,  the  equation  is  unchanged,  if  y  or  x  is 

increased  or  diminished  by  multiples  of  qyt. 

c.  If  either  /»  or  q  is  eve)t,  the   equation  is   unchanged   if  y  or  x  is 

increased  or  diminished  by  multiples  of  2q7r. 

d.  The  curve   repeats  in  the  direction  of  either  axis ;  at    intervals  of 

qTT  if  p  and  q  are  both  odd,  at  intervals  of  '2q7r  if  either  jd  or  q 
is  even. 


Neioton  and  Phillips  on  certain  'Iranscendental  Curves.       101 

e.  Straight  linos  itanvllel  to  y=i^.r  and  cutting  tlu'  axi's  at  intervals 
oiqn,  or  2fy7r,  according  as  ]>-\-q  is  even  or  odd,  belong  to  the 
locus  of  equation  (7). 

f.  Tliese  sti-aight  lines  divide  the   plane  of  coordinates  into  ecjual 

squares  for  any  given  value  of  m.  Each  square  contains  a 
similar  and  equal  portion  of  tlie  locus,  though  not  always 
siniilarly  placed, 

g.  Eqixation    (7)   is  satisfied    if  sin.v  sin?y^T=iO,   and  siny  siii///y— 0. 

Hence  the  locus  passes  through  all  the  angular  points  of  the 
rectangles  formed  by  these  two  series  of  parallel  straight  lines 
(Art.  7). 

h.  If  2^-\-Q  is  ^<^<^  isolated  points  appear,  belonging  to  the  locus,  at 
the  centers  of  the  squares. 

i.  The  maxima  and  minima  values  of  y  are  determined  by  the  equa- 
tion £- tan  a*:^  —  tan^^a?  (Art.  4,  c).  This  equation  represents 
q  q 

straight  lines  parallel  to  the  axis  of  y.      There  are  2(jij)  +  (/)  of 

the  lines  (Art.  4,  h)  in  an  interval  of  2q7T. 
j.  The  same  equation  in  y  gives  the  maxima  and  minima  values  of  x. 
k.  These  equations  are  also  the  conditions  of  the  isolated  and  double 

points.     Hence  there  can  be   isolated   or   double  points  only 

at  the  intersections  of  the  lines  i-  tan  xz=  —  tan  ^-x   with  the 

q  q 

lines  -L-  tany=:  —  tan  i-y. 
q  q 

I.  The  propositions  {i),  {J),  and  (k)  hold  equally  true  for  any  values 
of  a  and  b  in  equation  (1),  and  there  are  similar  properties  if  m 
is  not  equal  to  n. 

771.  The  figs.  48-65,  68,  and  70,  represent  curves  belonging  to  equa- 
tion (7).  Any  point  where  two  straight  lines  meet,  and  that  is 
surrounded  by  an  oval  may  be  the  origin. 

91.  Tf  through  the  double  points  on  the  line  y=:x  vertical  and  horizon- 
tal lines  be  di'awn,  these  lines  will  pass  through  all  the  points 
of  maxima  and  minima  ordinates  and  abscissas.  By  their 
intersections  they  will  mark  all  the  possible  positions  of  double 
points  for  any  values  of  a  and  b. 
12.  Equatio7i  (1)  lohen  a=l,  b=iO,  m-=.u=:an  irrational  number. 

The  equation 

sin  y  sin  \/i  y=sin  x  sin  \/i  ;r,  (8) 

represents  a  class  of  curves  tliat  do  not  repeat  their  forms  but  change 


102       N^ewtoii  CDid  Phillips  on  certain  Transcendental  Curves. 

continually  throughout  the  plane  of  coordinates.  The  curve  is  sym- 
metrical about  either  axis,  and  also  about  either  line  yz=.  i.e.  These 
two  lines  belong  to  the  curve. 

The  origin  and  a   portion   of  tlie  curve,    principally  in  the  first 
quadrant,  are  given  in  fig.  67,  ])late  XXII. 

13.  Equation  (1)  when  «— :  — 1,  JirzO,  ^/i=in-=  —     If  (j  is  eiwn  the 

equation 

sin  y  sin — y  =:  —  sm  x  sin  —x  (9) 

q  q 

merely  changes  the  sign  of  the  second  member  if  we  substitute  5';r -fa; 
for  X.  Hence  the  curves  in  figures  40,  42,  44,  and  47  represent  equa- 
tion (9),  when  q  is  eium,  the  origin  being  at  an  isolated  point. 

But  if  q  is  odd  we  obtain  new  forms  which  have  these  properties. 

a.  The  origin  is  an  isolated  point. 

b.  If  q=l,  the  locus  consists  solely  of  points  (fig.  39). 

c.  li  q=z3,  each  point  is  surrounded  by  one  closed  curve  (fig.  93). 

d.  If  q=5,  each  ^aoint  is  surrounded  by  two  closed  curves  (fig.  74). 

e.  The  resemblance   of  these  figvires  to   parts  of  figs.  40,  42,  and  44, 

and  the  law  ol'  their  formation  makes  it  unnecessary  to  give 
further  examples. 

f.  A  dot  and  four  suiTounding  closed  curves  in  fig.  47,  would  fairly 

represent  the  element  for  equation  (9),  when  ^1=9. 

14.  Equation  (1)  when  az=.  —  1,  5=0,  m:=.n=.  ^L.      Curves    whose 
equations  are  of  the  form 

sin  wsini^y=:  —  sin  x  sin  ^x  (10) 

q  q 

are  shown  in  figures  69,  71,  99,  and  108.  There  are  no  straight  lines 
belonging  to  the  locus.  The  origin  is  at  any  one  of  the  isolated 
points.  The  first  two  are  placed  beside  figures  68  and  70  for  ease  in 
comparing. 

The  following  propositions  of  Art.  11,  for  equation  (7)  apply  also 
to  equation  (10),  without  change  of  terms,  viz :  i,  c,  c7,  g.^  /,J,  and  h. 

15.  Equation  (1)  when  az=.\^  l>=0,  m=z],  and  ji=  i_  .     The  figures 

9' 
76-79,  and  81,  represent  curves  whose  equations  are 

siny  sin2/=sin£«sin-£--a;.  (11) 

9' 


Newton  ant/  JViiUips  on.  certain  Transcendental  Curuefi.       !();< 

Ill  tlu'  tlirection  of//  tliev  repeat  at  intervals  of  tt.  In  (ln'  direction 
of  .(•  they  repeat  at  intervals  of  qTT^  or  2(/'7r,  according  as  p'-\-q'  is 
even  or  odd. 

Fig.  80  gives  a  similar  cnrve  except  that  r/=  —  I. 

16.  Equation   (1)  idieji  a=^\,  b^=.0^  in-z  l^^-Mu\n,=:i-L.     The  eqna- 

q  q 

tion  (11)  is  a  special  case  of  the  equation 

sin  y  sin  ±- y  :=  sin  a;  sin  :^  a-.  (12) 

q  q' 

Examples  of  curves  from  equation  (12)  are  given  in  figures  82-91, 
123,  and  141.  The  number  of  different  curves  that  this  equation  gives 
us  is  quite  large,  even  if  q  and  q  are  limited  to  small  numbers.  If 
11  is  the  maximum  value  of  q  and  q' ,  the  number  of  inde]>endent 
curves  belonging  to  the  equation  is  nearly  a  thousand.  Equations  (5), 
(6),  (7)  and  (11)  are  special  cases  of  (12). 

IV.  Further  consideration  of  the  curves  of  equation  (12). 
a.  If  the  parallel  straight  lines  sin,r  sin:^ir=0  be  drawn  (Art.  7)  the 

plane  of  coordinates  is  divided  by  those  lines  into  portions. 
When  two  lines  coincide  the  portion  between  them  may  be 
regarded  as  real  but  infinitessimal.  In  crossing  any  of  these 
lines  the  sign  of  the  second  member  of  (12)  changes  from  plus 
to  minus,  or  vice-versa. 

h.  In  like  manner  in  crossing  any  of  the  parallel  lines  sin  y  sin  ^y=zO, 

^  q 

the  sign  ot  the  first  member  changes. 

c.  The  lines  dny  sin  ^(/--O,  and  sinic  sin^,r=0,  divide   the    plane 

q  q 

into  rectangles  (some  of  Avhieh  are  infinitessimal).  The  curve 
of  equation  (12)  passes  through  each  of  the  angular  points  of 
these  rectangles. 

d.  Since  the  signs  of  the  two  members  of  (12)  must  be  alike  the  curve 

passes  at  any  angle  of  a  rectangle  into  the  rectangle  vertically 
opposite.     It  passes  from  a  rectangle  only  at  the  angles. 

e.  If,   however,  any  rectangle  is   of  infinitessimal  breadth  and  finite 

length,  the  curve  at  its  extremity  becomes  tangent  to  the  line 

that  limits  the  infinitessimal  parallelogram. 
/.  If  a  rectangle  becomes  infinitessimal  in  both  directions,  the  curve 

has  at  that  point  an  isolated  or  a  double  point. 
f/.  The  horizontal    and   vertical    lines   of  fig.    148,  and  the  rectangles 

formed  by  them,  illustrate   the  above  propositions.     The  con- 


104       Nev:iton  and  Phillips  on  certain  Transcendental  Curves. 

tiiiuous  closed  line  represents  the  curve  of  equation  (12)  in  this 

case.     The  axis  of  y  is  the  heavy  vertical  line,  and  the  axis  of 

X  the  upper  heavy  horizontalline.     These  heavy  lines  are  double 

lines. 

h.  Several  of  the  propositions  of  Art.  11  apply  to  equation   (12)   with 

p  .  p' 

evident  modifications.     If  —  is  not  equal  to  — „    there     are    no 

straight  lines  belonging  to  the  locus. 

i.  We  may  regard  the  plane  of  the  curve  as  divided  into  equal 
rectangles  by  lines  parallel  to  the  axes,  the  altitudes  of  the 
rectangles  being  qrr,  or  25-7?,  according  as  p-\-q  is  even  or  odd, 
and  whose  bases  are  q'n,  or  25-' tt,  according  as  p'  -\-q'  is  even 
or  odd.  The  curve  (12)  repeats  itself  in  each  of  these  rectangles 
without  any  variation,  through  the  whole  extent  of  the  plane. 

j.  The  origin  of  (12)  is  a  real  double  point. 

18.  Effect  of  a  change  of  the  value  of  a  in  equation  {\),ichenb=iO. 
The  effect  of  a  change  in  the  value  of  the  coefficient  of  the  second 
member  may  be  observed  by  comparing  some  of  the  figures  :  for 
example,  figs.  38  with  39  ;  figs.  41  with  93  ;  figs.  45  with  72  and  73 ; 
figs.  77  with  80;  figs.  43  with  74  and  75  ;  figs.  123  with  131-135; 
figs.  136  with  141  and  145. 

1 9.  The  effect  of  the  change  of  this  factor  can  be  better  observet). 
in  the  simpler  equation 

sin  y= ^  sin  x,  (13) 

where  k  represents  a  as  assuming  several  values.  Figure  130  repre- 
sents a  faisceau  of  curves  for  equation  (13).  The  origin  is  the  nodal 
point  near  the  lower  left  hand  corner  of  the  figure.  Let  k  change 
from  —  cc  to  -j-  00  . 

a.  If  ^'rroo  ,  we  have  the  vertical  eqiiidistant  straight  lines. 

b.  If  k=.  —  2,  we  have  the  curved  lines  represented  by  uniform  fine 

dots.     At  the  origin  it  is  tangent  to  y=  —  2x. 

c.  If  A:=  — 1,  we    have  the  straight  lines  in  which  dots  and  strokes 

alternate. 

d.  If /<;—  — ^,  we  have  the  continuous  curved  lines. 

e.  If  A'-nO,  we  have  horizontal  straight  lines. 

f  If  k=:^,  we  have  the  heavy  dotted  curved  lines. 

g.  If  k=zl,  we  have  straight  lines  of  which  y=x  is  one,  and  the  others 

are  similarly  marked. 
A.  If  k=z2,  we  have  the  curved  lines  consisting  of  a  stroke  and  three 

dots  alternating. 


Newton  and  Phillips  on  certain  TransceMilental  Curves.        Kif) 

i.  If  X-=-|-a:,we  liaA'e  vertical  lines  iigaiii.  The  curve  is  at  the 
origin  always  tangent  to  yz=ikx.  The  faisceau  has  nodal  points 
wherever  .r  and  y  are  both  multiples  of  n. 

20.  If  we  consider  in  like  manner  the  faisceau  of  curves 

sin  y  sin  f y=:A;sin  x  sin  fit',  ( 1 4) 

for  various  values  of  k  (fig.  148),  we  shall  find  similar  but  more  com- 
plicated changes.  The  origin  is  the  intersection  of  the  heavy  lines 
near  the  top  of  the  figure.  The  figure  represents  the  loci  for  six 
values  of  Jc,  viz:  oc,  —1,  — |,  0,  +1,  and  -\-2.  Each  of  the  six  loci 
passes  through  each  nodal  point,  if  isolated  points  be  counted  as 
branches  of  a  locus. 

a.  For  kz=.  oc,  we  have  the  vertical  straight  lines.     The  heavy  line  is 

a  double  line. 

b.  For  k=.  —  1,  we  have  the  uniformly  dotted  curves. 

c.  For  k-=i — ^,  we  have  the  curves  represented  by  strokes  and  four 

dots  alternating. 

d.  For  X-=:0,  we  have  horizontal  straight  lines,  the  heavy  lines  being 

double. 

e.  For  A,=rl,  we  have  the  continuous  curves  (compare  fig.  14V). 

f.  For  A'=2,  we  have  the  curved  lines  consisting  of  a  long  stroke  and 

a  short  stroke  alternating. 

By  removal  upward  or  downward  a  distance  of  Stt,  the  curve  (b) 
coincides  with  (e).  In  general  any  one  of  the  curves  by  such  change 
coincides  with  that  one  for  which  k  has  an  equal  value  with  opposite 
sign. 

21.  We  may  in  like  manner  obtain  a  faisceau  of  curves  from  the 
equation 

sin  y  sin  my-^k  sin  x  sin  nx-\-b,  (15) 

by  giving  to  k  different  values. 

The  curve  will  be  the  horizontal  lines  siny  sin  myz=b  (Art.  8),  if 
kz=zO.  It  will  be  the  vertical  lines  sin  x  sin  mx=0,  if  kz=0.  For 
other  values  of  k,  the  curve  will  pass  through  all  the  points  of  inter- 
sections of  these  series  of  straight  lines.  Figure  66  represents  (with 
the  axes  interchanged)  the  vertical  and  horizontal  lines  in  a  special 
case. 

The  lines  of  maxima  and  minima  values  of  x  and  y,  and  the  pos- 
sible positions  of  double  points  (Art.  11,  i, ./,  k,),  are  independent  of 
k  and  b.     The  origin  is  not  upon  the  curve  if  k  and  b  are  finite. 

Trans.  Conn.  Acad.,  Vol.  III.  14  October,  1875. 


106        Newton  and  Phillips  on  certain  Transcendental  Curves. 

22.  Chayige  of  value  of  h  in  equation  {!).  It  remains  to  consider 
the  effect  of  a  change  in  the  constant  b  in  equation  (I).  That  it  may 
change  entirely  the  appearance  of  the  locus  will  be  seen  by  a  glance 
at  figures  92,  93,  and  94.  The  same  curves  are  superposed  in  fig.  95. 
Though  each  locus  may  have  its  own  double  points,  they  cannot 
when  superposed  cut  each  other. 

23.  In  the  figures  96-103,  the  curves  of  the  equation 

sin  y  sin  fi/=  —  sm  x  sin  ^x-\-k  (16) 

are  shown  for  certain  specified  values  of  k.  The  origin  is  the  place 
of  the  isolated  point  in  fig.  99.  The  several  curves  if  superposed  will 
not  intersect.  The  values  of  k  were  selected  so  as  to  furnish  curves 
with  double  points. 

24.  A  series  of  twelve  curves  from  the  equation 

sin y  sin x\y^  —sin x  sm^jX-\-k  (1 V) 

is  given  in  the  figures  104-115.  By  tracing  any  selected  portions  of 
the  figure  through  the  series  the  effect  of  the  change  in  k  will  be 
seen.  As  in  equation  (16)  values  of  k  were  chosen  which  give  (except 
fig.  108)  real  double  jDoints.  In  each  case  other  curves  of  the  series 
with  real  double  points  might  have  been  given. 

25.  Another  series  of  fourteen  curves  is  given  in  figures  116-129 
from  the  equation 

sin  y  sin ^y=sm x  s'm^x-{-k.  (18) 

The  complete  series  would  give  18  curves  with  double  or  isolated 
points.  The  omitted  curves  are  those  having  isolated  points,  one  at 
the  beginning  and  one  at  the  end  of  the  series,  one  between  figs.  127 
and  128,  and  one  between  figs.  129  and  130. 

26.  Similar  partial  series  can  be  seen  in  figs.  136-138,  in  figs. 
139-143,  and  in  figs.  144-146. 

27.  The  superposition  of  the  several  curves  of  a  series  is  shown  in 
figure  147  where  the  curves  represent  the  equation 

sin y  sin  f  y=  sin  x  sin  fx-\-l: 
A  little  more  than  one  complete  figure  of  the  curves  is  shown.     The 
oi-igin  is  at  the  double  point  near  the  top  of  the  figure.     The  value  of 
k  varies  from  curve  to  curve  by  intervals  of  -i^,  and  it  cannot  numeri- 
cally exceed  2,     The  full  line  corresponds  to  kz=0. 

The  multiple  that  k  is  of  -j-^  is  denoted  by  the  number  of  dots 
between  the  long  strokes  of  the  lines. 

The  multiple  that  k  is  of  —  i  is  denoted  by  the  number  of  short 
strokes  between  the  long  strokes  in  the  lines. 


JVewtou  and  l*/ifl//ps  on  certain  Transcendental  Curves.       lOT 

28.  The  resemblance  of  lig.  147  to  a  series  of  contour  lines  in  sur- 
veying, suggests  a  corresponding  treatment  of  the  equation.     Let 

2:=sin//  sin/y?y— asina-  ^mn.r—b  (19) 

be  the  equation  of  a  surface,  and  let  it  be  intersected  by  planes 
parallel  to  the  plane  of  .*-y,  and  we  may  obtain  the  groups  of  curves 
described  in  Arts.  22-27. 

The  surface  of  equation  (19)  may  be  described  by  continuous  mo- 
tion, as  follows  :  Let  sr=:siny  sin  my  be  a  plane  curve  (figs.  1-37),  and 
let  it  move  parallel  to  itself  so  that  each  point  of  it  shall  describe  a 
straight  line  parallel  to  the  axis  of  .v.  The  curve  shall  then  describe 
a  cylindrical  surface  whose  equation  is 

zz=.%mi/  •t^mtny.  (20) 

Let  z=z  —  am\x^\\\nx  —  b  be  the  equation  of  a  second  plane  curve, 
and  let  this  curve  move  parallel  to  the  plane  xz,  in  such  a  manner 
that  the  axis  of  x  of  the  curve  shall  always  lie  in  the  cylindrical  sur- 
face (20),  The  curve  will  describe  by  its  motion  the  surface  of 
equation  (19). 

The  surface  will  consist  of  one  contini;ous  sheet  lying  between  the 
two  parallel  planes  sr^it  (l  +  ^-j-^'*),  the  positive  numerical  values  of 
a  and  h  being  here  taken. 

29.  By  means  of  the  two  arbitrary  constants,  a  and  h,  in  equation 
(1)  the  curve  may  be  made  to  pass  through  any  two  points  of  the 
plane. 

In  a  rectangle  whose  base  is  2*7' ;r,  and  altitude  IqTt,  there  are 
'^{p-\-q){p' -\-q')  possible  positions  of  double  points  (Art.  11,  k.)  If 
the  curve  passes  through  such  a  point  it  must  have  there  two  branches 
real  or  imaginary. 

Hence  we  may  assign  to  a  and  b  such  values  that  the  curve  will 
have  double  points,  in  general,  at  any  two  of  the  ^{l^-\-q){l)'-{-q') 
possible  positions. 


ERRATUM   m   PLATE   XVI. 

In  figure  40,  plate  XVI,  there  is  a  series  of  ovals  about  one-half  of  the  real  double 
points.  There  should  be  added  to  the  curve,  as  represented,  a  like  series  of  ovals 
around  each  of  the  remaining  real  double  points. 


v.   On  the  Equilibrium  of  Heterogeneous  Substances. 

By    J.    WlLLARD     GiBBS. 

"Die  Energie  der  Welt  ist  constant. 
Die  Entropie  der  Welt  strebt  elnem  Maximum  zu." 

Clausius.* 

The  comprehension  of  the  hiws  which  govern  any  material  system 
is  greatly  facilitated  by  considering  the  energy  and  entropy  of  the 
system  in  the  various  states  of  which  it  is  capable.  As  the  difference 
of  the  values  of  the  energy  for  any  two  states  represents  the  com- 
bined amount  of  work  and  heat  received  or  yielded  by  the  system 
when  it  is  brought  from  one  state  to  the  other,  and  the  difference  of 

entropy  is  the  limit  of  all  the  possible  values  of  the  integral   I  -t'-i 

{dQ  denoting  the  element  of  the  heat  received  from  external  sources, 
and  t  the  temperature  of  the  part  of  the  system  receiving  it,)  the 
varying  values  of  the  energy  and  entropy  characterize  in  all  that  is 
essential  the  effects  producible  by  the  system  in  passing  from  one 
state  to  another.  For  by  mechanical  and  thermodynamic  con- 
trivances, supposed  theoretically  perfect,  any  supply  of  work  and 
heat  may  be  transformed  into  any  other  which  does  not  differ  from 
it  either  in  the  amount  of  work  and  heat  taken  together  or  in   the 

value  of  the  integral  /  — —.      But  it  is  not   only  in   respect  to  the 

extei'ual  relations  of  a  system  that  its  energy  and  entropy  are  of 
predominant  importance.  As  in  the  case  of  simply  mechanical  sys- 
tems, (such  as  are  discussed  in  theoretical  mechanics,)  which  are  capable 
of  only  one  kind  of  action  upon  external  systems,  viz.,  the  perform- 
ance of  mechanical  work,  the  function  which  expresses  the  capability 
of  the  system  for  this  kind  of  action  also  plays  the  leading  part  in 
the  theory  of  equilibrium,  the  condition  of  equilibrium  being  that 
the  variation  of  this  function  shall  vanish,  so  in  a  thermodynamic 
system,  (such  as  all  material  systems  actually  are,)  which  is  capable  of 
two  different  kinds  of  action  upon  external  systems,  the  two  functions 
which  express  the  twofold  capabilities  of  the  system  afford  an  almost 
equally  simple  criterion  of  equilibrium. 

*Pogg.  Ann.  Bd.  cxxv  (1865),  S.  400;  or  Mechanische  Warmetheorie,  Abhand.  ix.,  S.  44. 


J.  W.  Gihhs — Equilibrium  of  Heterogeneous  Substances.      109 

CRITERIA    OP    EQUlLIBRIUiM    AND    STABILITY. 

Tlie  criterion  of  equilibrium  for  a  material  system  Avhicli  is  isolated 
from  all  external  influences  may  be  expressed  in  either  of  the  follow- 
ing entirely  equivalent  forms : 

I.  M>r  the  equilibrium  of  any  isolated  si/stem  it  is  necesmn/  and 
sufficient  that  in  all  possible  variations  of  tlie  state  of  the  system 
which  do  not  alter  its  energy^  the  variation  of  its  entropy  shall  either 
vanish  or  be  negative.  If  e  denote  the  energy,  and  ;/  the  entropy  of 
the  system,  and  we  use  a  subscript  letter  after  a  variation  to  indicate 
a  quantity  of  which  the  value  is  not  to  be  varied,  the  condition  of 
equilibrium  may  be  written 

{^V)e  ^0-  (1) 

II.  For  the  equilibrium  of  any  isolated  system  it  is  7iecessary  and 
sufficient  that  in  cdl  possible  variations  in  the  state  of  the  system 
which  do  not  alter  its  entropy^  the  variation  of  its  energy  shall  either 
vanish  or  be  positive.     This  condition  may  be  written 

(d>),^  0.  (2) 

That  these  two  theorems  are  equivalent  will  appear  from  the  con- 
sideration that  it  is  always  possible  to  increase  both  the  energy  and 
the  entropy  of  the  system,  or  to  decrease  both  together,  viz.,  by 
imparting  heat  to  any  part  of  the  system  or  by  taking  it  away.  For, 
if  condition  (l)  is  not  satisfied,  there  must  be  some  variation  in  the 
state  of  the  system  for  which 

6i]  >  0  and  de  =zQ; 
therefore,  by  diminishing  both  the  energy  and  the  entropy  of  the 
system  in  its  varied  state,  we  shall  obtain  a  state  for  which  (considered 
as  a  variation  from  the  original  state) 

6i]z=i  0  and  (^f  <0; 
therefore  condition  (2)  is  not  satisfied.     Conversely,  if  condition  (2) 
is  not  satisfied,  there  must  be  a  variation  in  the  state  of  the  system 

for  which 

(Jf  <  0  and  6i]^^0\ 

hence  there  must  also  be  one  for  which 

^f  rz:  0  and  (J//  >  0  ; 

therefore  condition  (1)  is  not  satisfied. 

The  equations  which  express  the  condition  of  equilibrium,  as  also 
its  statement  in  words,  are  to  be  interpreted  in  accordance  with  the 
o-eneral  usage  in  respect  to  differential  equations,  that  is,  infinitesimals 


110      J.W.  Gibbs — Equilihriiim  of  Heterogeneous  Suhsta7ices. 

of  higher  orders  than  the  first  relatively  to  those  which  express  the 
amount  of  change  of  the  system  are  to  be  neglected.  Biit  to  distin- 
guish the  dilFerent  kinds  of  equiliVjriam  in  respect  to  stability,  we 
must  have  regard  to  the  absolute  values  of  the  variations.  We  will 
use  A  as  the  sign  of  variation  in  those  equations  which  are  to  be  con- 
strued strictly,  i.  e.,  in  which  infinitesimals  of  the  higher  orders  are 
not  to  be  neglected.  With  this  understanding,  Ave  may  express  the 
necessary  and  sufticient  conditions  of  the  difi:erent  kinds  of  equi- 
librium as  follows; — for  stable  equilibrium 

(^V)e<0,  i.e.,  (A^),^>0:  (3) 

for  neutral  equilibrium  there  must  be  some  variations  in  the  state  of 
the  system  for  which 

(A//)^:=rO,  i.  e.,  {A5)^^  =  0,  (4) 

while  in  general 

(^V)e  ^0,  i.e.,  (A£)^^0;  (5) 

and  for  unstable  equilibrium  tliere  must  be  some  variations  for  which 

(A;;),>0,  (6) 

i.  e.,  there  must  be  some  for  which 

(^f),<0,  "  (V) 

while  in  general 

((^;/),^0,i.e,  (^6),^0.  (8) 

In  these  criteria  of  equilibrium  and  stability,  account  is  taken  only 
oi possible  variatic>ns.  It  is  necessary  to  explain  in  what  sense  this  is 
to  be  understood.  In  the  first  place,  all  variations  in  the  state  of 
the  system  which  involve  the  transportation  of  any  matter  through 
any  finite  distance  are  of  course  to  be  excluded  from  consideration, 
although  they  may  be  capable  of  expression  by  infinitesimal  varia- 
tions of  quantities  which  perfectly  determine  the  state  of  the  system. 
For  example,  if  the  system  contains  two  masses  of  the  same  sub- 
stance, not  in  contact,  nor  connected  by  other  masses  consisting  of 
or  containing  the  same  substance  or  its  components,  an  infinitesimal 
increase  of  the  one  mass  with  an  equal  decrease  of  the  other  is  not  to 
be  considered  as  a  possible  variation  in  the  state  of  the  system.  In 
addition  to  such  cases  of  essential  impossibility,  if  heat  can  pass  by 
conduction  or  radiation  from  every  j^art  of  the  system  to  every  other, 
only  those  variations  are  to  be  rejected  as  impossible,  which  involve 
changes  which  are  prevented  by  passive  forces  or  analogous  resist- 
ances to  change.  But,  if  the  system  consist  of  parts  between  which 
there  is  supposed  to  be  no  thermal  communication,  it  will  be  neces- 
sary to  regard  as  impossible  any  diminution  of  the  entropy  of  any  of 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Sub.^taxces.      11] 

tliese  parts,  as  sueli  a  change  can  not  take  place  witliout  the  passage 
of  heat.  This  limitation  may  most  conveniently  he  applied  to  the 
second  of  the  above  forms  of  the  condition  of  equilibrium,  which  will 
then  become 

(^^V,  ;/",  etc.  =  t*.  (9) 

?/,  //",  etc.,  denoting  the  entropies  of  the  various  parts  between  which 
there  is  no  communication  of  heat.  When  the  condition  of  equi- 
librium is  thus  expressed,  the  limitation  in  respect  to  the  conduction 
of  heat  will  need  no  farther  consideration. 

In  order  to  apply  to  any  system  the  criteria  of  equilibriiim  which 
have  been  given,  a  knowledge  is  requisite  of  its  passive  forces  or 
resistances  to  change,  in  so  far,  at  least,  as  they  are  capable  of  pre- 
venting  change.  (Those  passive  forces  which  only  retard  change, 
like  viscosity,  need  not  be  considered.)  Such  properties  of  a  system 
are  in  general  easily  recognized  upon  the  most  superficial  knowledge 
of  its  nature.  As  examples,  we  may  instance  the  passive  force  of 
friction  which  prevents  sliding  when  two  surfaces  of  solids  are 
pressed  together, — that  which  prevents  the  different  components  of 
a  solid,  and  sometimes  of  a  fluid,  from  having  different  motions  one 
from  another, — that  resistance  to  change  which  sometimes  prevents 
either  of  two  forms  of  the  same  substance  (simple  or  compound), 
which  are  capable  of  existing,  from  passing  into  the  other, — that 
which  prevents  the  changes  in  solids  which  imply  plasticity,  (in  other 
words,  changes  of  the  form  to  which  tlie  solid  tends  to  return,)  when 
the  deformation  does  not  exceed  certain  limits. 

It  is  a  characteristic  of  all  these  passive  resistances  that  they  pre- 
vent a  certain  kind  of  motion  or  change,  however  the  initial  state  of 
the  system  may  be  modified,  and  to  whatever  external  agencies  of  force 
and  heat  it  may  be  subjected,  within  limits,  it  may  be,  but  yet  within 
limits  which  allow  finite  variations  in  the  values  of  all  the  quanti- 
ties which  express  the  initial  state  of  the  system  or  the  mechanical 
or  thermal  influences  acting  on  it,  without  producing  the  change  in 
question.  The  equilibrium  which  is  due  to  such  passive  properties 
is  thus  widely  distinguished  from  that  caused  by  the  balance  of  the 
active  tendencies  of  the  system,  where  an  external  influence,  or  a 
change  in  the  initial  state,  infinitesimal  in  amount,  is  sufticient  to  pro- 
duce change  either  in  the  positi^-e  or  negative  direction.  Hence  the 
ease  with  which  these  passive  resistances  are  recognized.  Only  in 
the  case  that  the  state  of  the  system  lies  so  near  the  limit  at  which 
the  resistances  cease  to  be  operative  to  prevent  change,  as  to  create  a 


112      tT.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances. 

doubt  whether  the  case  falls  within  or  witliout  the  limit,  will  a  moi'e 
accurate  knowledge  of  these  resistances  be  necessary. 

To  establisli  the  validity  of  the  criterion  of  equilibrium,  we  will 
consider  first  the  sufficiency,  and  afterwards  the  necessity,  of  the  con- 
dition as  expressed  in  either  of  the  two  equivalent  forms. 

In  the  first  place,  if  the  system  is  in  a  state  in  which  its  entropy  is 
greater  than  in  any  other  state  of  the  same  energy,  it  is  evidently  in 
equilibrium,  as  any  change  of  state  must  involve  either  a  decrease  of 
entropy  or  an  increase  ot  energy,  which  are  alike  impossible  for  an  iso- 
lated system..  We  may  add  that  this  is  a  case  of  stable  equilibrium,  as 
no  infinitely  small  cause  (whether  relating  to  a  variation  of  the  initial 
state  or  to  the  action  of  any  external  bodies)  can  produce  a  finite 
change  of  state,  as  this  Avould  involve  a  finite  decrease  of  entropy  or 
increase  of  energy. 

We  will  next  suppose  that  the  system  has  the  greatest  entropy 
consistent  with  its  energy,  and  therefore  the  least  energy  consistent 
with  its  entropy,  but  that  there  are  other  states  of  the  same  energy 
and  entropy  as  its  actual  state.  In  this  case,  it  is  impossible  that 
any  motion  of  masses  should  take  place ;  for  if  any  of  the  energy 
of  the  system  should  come  to  consist  of  vis  viva  (of  sensible  motions), 
a  state  of  the  system  identical  in  other  respects  but  without  the 
motion  would  have  less  energy  and  not  less  entropy,  which  would  be 
contrary  to  the  supposition.  (But  we  cannot  apply  this  reasoning  J,o 
the  motion  within  any  mass  of  its  different  components  in  different 
directions,  as  in  diffiision,  when  the  momenta  of  the  components 
balance  one  another.)  Nor,  in  the  case  supposed,  can  any  conduction 
of  heat  take  place,  for  this  involves  an  increase  of  entropy,  as  heat  is 
only  conducted  from  bodies  of  higher  to  those  of  lower  temperature. 
It  is  equally  impossible  that  any  changes  should  be  produced  by  the 
transfer  of  heat  by  radiation.  The  condition  which  we  have  sup- 
posed is  therefore  sufficient  for  equilibrium,  so  far  as  the  motion  of 
masses  and  the  transfer  of  heat  are  concerned,  but  to  show  that  the 
same  is  true  in  regard  to  the  motions  of  diffusion  and  chemical  or 
molecular  changes,  when  these  can  occur  without  being  accompanied 
or  followed  by  the  motions  of  masses  or  the  transfer  of  heat,  we  must 
have  recourse  to  considerations  of  a  more  general  nature.  The  fol- 
lowing considerations  seem  to  justify  the  belief  that  the  condition  is 
sufficient  for  equilibrium  in  every  respect. 

Let  us  suppose,  in  order  to  test  the  tenability  of  such  a  hypothesis, 
that  a  system  may  have  the  greatest  entropy  consistent  with  its 
energy  without  being  in  equilibrium.     In  such  a  case,  changes  in  the 


J,  W.  Gihhs — Equilihrkmi  of  Heterogeneous  Substances.      113 

state  of  the  system  must  take  place,  but  these  will  necessarily  be 
such  that  the  energy  and  the  entropy  will  remain  unchanged  and 
the  system  will  continue  to  satisfy  the  same  condition,  as  initially,  of 
having  the  greatest  entropy  consistent  with  its  energy.  Let  us  con- 
sider the  change  which  takes  place  in  any  time  so  short  that  the 
change  may  be  regarded  as  uniform  in  nature  throughout  that  time. 
This  time  must  be  so  chosen  that  the  change  does  not  take  place  in  it 
infinitely  slowly,  which  is  always  easy,  as  the  change  which  we  sup- 
pose to  take  place  cannot  be  infinitely  slow  except  at  particular 
moments.  Now  no  change  whatever  in  the  state  of  the  system, 
which  does  not  alter  the  value  of  the  energy,  and  which  commences 
with  the  same  state  in  which  the  system  was  supposed  at  the  com- 
mencement of  the  short  time  considered,  will  cause  an  increase  of 
entropy.  Hence,  it  Avill  generally  be  possible  by  some  slight  varia- 
tion in  the  circumstances  of  the  case  to  make  all  changes  in  the  state 
of  the  system  like  or  nearly  like  that  which  is  supposed  actually  to 
occur,  and  not  involving  a  change  of  energy,  to  involve  a  necessary 
decrease  of  entropy,  which  would  render  any  such  change  impossible. 
This  variation  may  be  in  the  values  of  the  variables  which  determine 
the  state  of  the  system,  or  in  the  values  of  the  constants  which  deter- 
mine the  nature  of  the  system,  or  in  the  form  of  the  functions  which 
express  its  laws, — only  there  must  be  nothing  in  the  system  as  modi- 
fied which  is  thermodynamically  impossible.  For  example,  we  might 
suppose  teraperatiire  or  pressure  to  be  varied,  or  the  composition  of 
the  diiFerent  bodies  in  the  system,  or,  if  no  small  variations  which 
could  be  actually  realized  would  produce  the  required  result,  we 
might  suppose  the  properties  themselves  of  the  substances  to  undergo 
variation,  subject  to  the  general  laws  of  matter.  If,  then,  there  is 
any  tendency  toward  change  in  the  system  as  first  supposed,  it  is  a 
tendency  which  can  be  entirely  checked  by  an  infinitesimal  variation 
in  the  circumstances  of  the  case.  As  this  supposition  cannot  be 
allowed,  we  must  believe  that  a  system  is  always  in  equilibrium 
when  it  has  the  greatest  entropy  consistent  with  its  energy,  or,  in 
other  words,  when  it  has  the  least  energy  consistent  with  its  entropy. 

The  same  considerations  will  evidently  apply  to  any  case  in  which 
a  system  is  in  such  a  state  that  A;?  ^  0  for  any  possible  infinites- 
imal variation  of  the  state  for  which  Ae=  0,  even  if  the  entropy  is 
not  the  least  of  which  the  system  is  capable  with  the  same  energy. 
(The  term  possible  has  here  the  meaning  previously  defined,  and  the 
character  A  is  used,  as  before,  to  denote  that  the  equations  are  to  be 

Trans.  Conn.  Acad.,  Vol.  III.  15  October,  1875. 


114      '/.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 

construed  strictly,  i.  e.,  without  neglect  of  the  infinitesimals  of  the 
higher  orders.) 

The  only  case  in  which  the  sufficiency  of  the  condition  of  equi- 
librium which  has  been  given  remains  to  be  proved  is  that  in  which 
in  our  notation  dj]  ^  0  for  all  possible  variations  not  affecting  the 
energy,  but  for  some  of  these  variations  A//  >  0,  that  is,  when  the 
entroj^y  has  in  some  respects  the  characteristics  of  a  minimum.  In 
this  case  the  considerations  adduced  in  the  last  paragraph  will  not 
apply  without  modification,  as  the  change  of  state  may  be  infinitely 
slow  at  first,  and  it  is  only  in  the  initial  state  that  the  condition 
Sr^^  -S  0  holds  true.  But  the  differential  coefficients  of  all  orders  of 
the  quantities  which  determine  the  state  of  the  system,  taken  with 
respect  of  the  time,  must  be  functions  of  these  same  quantities. 
None  of  these  differential  coefficients  can  have  any  value  other  than 
0,  for  the  state  of  the  system  for  which  8ri^  ^0.  For  otherwise,  as 
it  would  generally  be  possible,  as  before,  by  some  infinitely  small 
modification  of  the  case,  to  render  impossible  any  change  like  or  nearly 
like  that  which  might  be  supposed  to  occur,  this  infinitely  small 
modification  of  the  case  would  make  a  finite  difference  in  the  value 
of  the  differential  coefficients  which  had  before  the  finite  values,  or 
in  some  of  lower  orders,  which  is  contrary  to  that  continuity  which 
we  have  reason  to  expect.  Such  considerations  seem  to  justify  us 
in  regarding  such  a  state  as  we  are  discussing  as  one  of  theoretical 
equilibrium ;  although  as  the  equilibrium  is  evidently  unstable,  it 
cannot  be  realized. 

We  have  still  to  prove  that  the  condition  enunciated  is  in  every 
case  necessary  for  equilibrium.  It  is  evidently  so  in  all  cases  in 
which  the  active  tendencies  of  the  system  are  so  balanced  that 
changes  of  every  kind,  except  those  excluded  in  the  statement  of 
the  condition  of  equilibrium,  can  take  place  reversibly,  (i.  e.,  both  in 
the  positive  and  the  negative  direction,)  in  states  of  the  system  dif- 
fering infinitely  little  from  the  state  in  question.  In  this  case,  we 
may  omit  the  sign  of  inequality  and  write  as  the  condition  of  such  a 
state  of  equilibrium 

(0»,rr:0,     i.e.,     {6e\  =  0  (10) 

But  to  prove  that  the  condition  previously  enunciated  is  in  every 
case  necessary,  it  must  be  shown  that  whenever  an  isolated  system 
remains  without  change,  if  there  is  any  infinitesimal  variation  in  its 
state,  not  involving  a  finite  change  of  position  of  any  (even  an  infini- 
tesimal part)  of  its  matter,  which  would  diminish   its   energy  by  a 


J.  ir.  Gihhs — Equilibrium  of  Heterogeneous  Substances.      115 

quantity  which  is  not  infinitely  small  relatiA^ely  to  the  variations 
of  the  quantities  which  determine  tlie  state  of  the  system,  without 
altering  its  entropy,— or,  if  the  system  has  thermally  isolated  parts, 
without  altering  the  entropy  of  any  such  part, — this  variation 
involves  changes  in  the  system  which  are  prevented  by  its  passive 
forces  or  analogous  resistances  to  change.  Now,  as  the  described 
variation  in  the  state  of  the  system  diminishes  its  energy  without 
altering  its  entropy,  it  must  be  regarded  as  theoretically  possible  to 
produce  that  variation  by  some  process,  perhaps  a  very  indirect  one, 
so  as  to  gain  a  certain  amount  of  work  (above  all  expended  on  the 
system).  Hence  we  may  conclude  that  the  active  forces  or  tenden- 
cies of  the  system  favor  the  variation  in  question,  and  that  equi- 
librium cannot  subsist  unless  the  variation  is  prevented  by  passive 
forces. 

The  preceding  considerations  will  suffice,  it  is  believed,  to  establish 
the  validity  of  the  criterion  of  equilibrium  which  has  been  given. 
The  criteria  of  stability  may  readily  be  deduced  from  that  of  equi- 
librium. We  will  now  proceed  to  apjily  these  principles  to  systems 
consisting  of  heterogeneous  substances  and  deduce  the  special  laws 
which  apply  to  different  classes  of  phenomena.  For  this  purpose  we 
shall  use  the  second  form  of  the  criterion  of  equilibrium,  both  because 
it  admits  more  readily  the  introduction  of  the  condition  that  there 
shall  be  no  thermal  communication  between  the  different  parts  of  the 
system,  and  because  it  is  more  convenient,  as  respects  the  form  of 
the  general  equations  relating  to  equilibrium,  to  make  the  entropy 
one  of  the  independent  variables  which  determine  the  state  of  the 
system,  than  to  make  the  energy  one  of  these  variables. 

THE    CONDITIONS    OF     EQUILIBRIUiNt     FOR     HETEROGENEOUS     MASSES     IN 

CONTACT    WHEN    UNIXFLtTENCED  BY  GRAVITY,  ELECTRICITY,  DISTORTION 

OF    THE    SOLID    MASSES,    OR    CAPILLARY    TENSIONS. 

In  order  to  arrive  as  directly  as  })ossible  at  the  most  characteristic 
and  essential  laws  of  chemical  equilibrium,  we  will  first  give  our 
attention  to  a  case  of  the  simplest  kind.  We  will  examine  the  con- 
ditions of  equilibrium  of  a  mass  of  matter  of  various  kinds  enclosed 
in  a  rigid  and  fixed  envelop,  which  is  impermeable  to  and  unalter- 
able by  any  of  the  substances  enclosed,  and  perfectly  non-conducting 
to  heat.  We  will  suppose  that  the  case  is  not  complicated  by  the 
action  of  gravity,  or  by  any  electrical  influences,  and  that  in  the 
solid  portions  of  the  mass  the  pressure  is  the  same  in  every  direction. 


116      J.  W.  Glbbs — Equilihrium  of  Heterogeneous  Substances. 

We  will  farther  simplify  the  problem  by  supposing  that  the  varia- 
tions of  the  parts  of  the  energy  and  entropy  which  depend  upon  the 
surfaces  separating  heterogeneous  masses  are  so  small  in  comparison 
with  the  variations  of  the  parts  of  the  energy  and  entropy  which 
depend  upon  the  quantities  of  these  masses,  that  the  former  may  be 
neglected  by  the  side  of  the  latter;  in  other  words,  we  will  exclude 
the  considerations  which  belong  to  the  theory  of  capillarity. 

It  will  be  observed  that  the  siipposition  of  a  rigid  and  non- 
conducting envelop  enclosing  the  mass  under  discussion  involves  no 
real  loss  of  genei-ality,  for  if  any  mass  of  matter  is  in  equilibrium,  it 
would  also  be  so,  if  the  whole  or  any  part  of  it  were  enclosed  in  an 
envelop  as  supposed ;  therefore  the  conditions  of  equilibrium  for  a 
mass  thus  enclosed  are  the  general  conditions  which  must  always 
be  satisfied  in  case  of  equilibrium.  As  for  the  other  suppositions 
which  have  been  made,  all  the  circumstances  and  considerations 
which  are  here  excluded  will  afterward  be  made  the  subject  of 
special  discussion. 

Conditions  relating  to  the  Equilibrium  between  the  initially  existing 
Hoinogeneons  Partt^  of  the  given  Mass. 

Let  us  first  consider  the  energy  of  any  homogeneous  part  of  the 
given  mass,  and  its  variation  for  any  j^ossible  variation  in  the  com- 
position and  state  of  this  part.  (By  homogeneous  is  meant  that  the 
part  in  question  is  uniform  throughout,  not  only  in  chemical  com- 
position, but  also  in  physical  state.)  If  we  consider  the  amount  and 
kind  of  matter  in  this  homogeneous  mass  as  fixed,  its  energy  5  is  a 
function  of  its  entropy  ?/,  and  its  volume  v,  and  the  differentials 
of  these  quantities  are  subject  to  the  relation 

ds.  ■=.  t  di]  -  •  p  dv .,  (11) 

t  denoting  the  (absolute)  temperature  of  the  mass,  and  p  its  pressure. 
For  t  di]  is  the  heat  received,  and  p  do  the  work  done,  by  the  mass 
during  its  change  of  state.  But  if  we  consider  the  matter  in  the 
mass  as  variable,  and  write  mj,  jn^,  .  .  .  m„  for  the  quantities  of  the 
various  substances  /S'j,  /Sg,  .  .  .  N„  of  which  the  mass  is  composed,  s 
will  evidently  be  a  function  of  //,  v,  m^.,  ^2,  .  .  .  ?>?„,  and  we  shall 
have  for  the  complete  value  of  the  differential  of  e 

de:=ztdi]  —  pdv -{- f.i^dm^-\- I.i.,dm2  .  .  .  -|-//„(?ot„,  (12) 
yUj,  yWg,  .  .  .  //„  denoting  the  diflferential  coefficients  of  s  taken  with 
respect  to  m,,  nio,  .  .  .  m„. 

The  substances  /S',,  62,  .  .  .  /S'„,  of  which  we  consider  the  mass 
composed,  must  of  course  be  such  that  the  values  of   the  differen- 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.      Il7 

tials  c?mj,  dm^.,  .  .  .  dm^  shall  be  indeiDendent,  and  shall  express 
every  possible  variation  in  the  composition  of  the  homogeneous  mass 
considered,  including  those  produced  by  the  absorption  of  substances 
different  from  any  initially  pi-esent.  It  may  therefore  be  necessary 
to  have  terms  in  the  equation  relating  to  component  substances 
which  do  not  initially  occur  in  the  homogeneous  mass  considered, 
provided,  of  course,  that  these  substances,  or  their  components,  are 
to  be  found  in  some  part  of  the  whole  given  mass. 

If  the  conditions  mentioned  are  satisfied,  the  choice  of  the  sub- 
stances which  we  are  to  i-egard  as  the  components  of  the  mass  con- 
sidered, may  be  determined  entirely  by  convenience,  and  independently 
of  any  theory  in  regard  to  the  internal  constitution  of  the  mass.  The 
number  of  components  will  sometimes  be  greater,  and  sometimes 
less,  than  the  number  of  chemical  elements  present.  For  example, 
in  considering  the  equilibrium  in  a  vessel  containing  water  and  free 
hydrogen  and  oxygen,  we  should  be  obliged  to  recognize  three  com- 
ponents in  the  gaseous  part.  But  in  considering  the  equilibrium  of 
dihite  sulphuric  acid  with  the  vapor  which  it  yields,  we  shoiild  have 
only  two  components  to  consider  in  the  liquid  mass,  sulphuric  acid 
(anhydrous,  or  of  any  particular  degree  of  concentration)  and  (addi- 
tional) water.  If,  however,  we  are  considering  sulphuric  acid  in  a 
state  of  maximum  concentration  in  connection  with  substances  which 
might  possibly  afford  water  to  the  acid,  it  must  be  noticed  that  the 
condition  of  the  independence  of  the  differentials  will  require  that  we 
consider  the  acid  in  the  state  of  maximum  concentration  as  one  of 
the  components.  The  quantity  of  this  component  will  then  be  capa- 
ble of  variation  both  in  the  positive  and  in  the  negative  sense,  while 
the  quantity  of  the  other  component  can  increase  but  cannot  decrease 
below  the  value  0. 

For  brevity's  sake,  we  may  call  a  substance  S^  an  actual  component 
of  any  homogeneous  mass,  to  denote  that  the  quantity  ra^  of  that 
substance  in  the  given  mass  may  be  either  increased  or  diminished 
(although  we  may  have  so  chosen  the  other  component  substances 
that  m^  =.  0) ;  and  we  may  call  a  substance  S^  a  possible  component 
to  denote  that  it  may  be  combined  with,  but  cannot  be  substracted 
from  the  homogeneous  mass  in  question.  In  this  case,  as  we  have 
seen  in  the  above  example,  we  must  so  choose  the  component  sub- 
stances that  Wj  rz  0. 

The  units  by  which  we  measure  the  substances  of  which  we  regard 
the  given  mass  as  composed  may  each  be  chosen  independently.  To 
fix  our  ideas  for  the  purpose  of  a  general  discussion,  we  may  suppose 


118      J.  W.  Gihhs — Equilibrium  of  Heterogeneous  Substances. 

all  substances  measured  by  weight  oi'  mass.  Yet  in  special  cases,  it 
may  be  more  convenient  to  adopt  chemical  equivalents  as  the  units 
of  the  component  substances. 

It  may  be  observed  that  it  is  not  necessary  for  the  validity  of 
equation  (12)  that  the  variations  of  nature  and  state  of  the  mass  to 
which  the  equation  refers  should  be  such  as  do  not  disturb  its  homo- 
geneity, provided  that  in  all  parts  of  the  mass  the  variations  of 
nature  and  state  are  infinitely  small.  For,  if  this  last  condition  be 
not  violated,  an  equation  like  (12)  is  certainly  valid  for  all  the  infin- 
itesimal parts  of  the  (initially)  homogeneous  mass;  i.  e.,  if  we  write 
2>f,  Z>//,  etc.,  for  the  energy,  entropy,  etc.,  of  any  infinitesimal  part, 

dDe  =  t  dDt]  -  p  dBv  -\-  /<  ^  dDm  ^-\-  fi.^  dJDni^ ...-{-/'« dDm„^    (13) 

whence  we  may  derive  equation  (12)  by  integrating  for  the  whole 
initially  homogeneous  mass. 

We  will  now  suppose  that  the  whole  mass  is  divided  into  parts  so 
that  each  part  is  homogeneous,  and  consider  such  variations  in  the 
energy  of  the  system  as  are  due  to  variations  in  the  composition  and 
state  of  the  several  parts  i*emaining  (at  least  approximately)  homoge- 
neous, and  together  occupying  the  whole  space  within  the  envelop. 
We  will  at  first  suppose  the  case  to  be  such  that  the  component  sub- 
stances are  the  same  for  each  of  the  parts,  each  of  the  substances 
aSj,  *S'2,  .  .  .  Sn  being  an  actual  component  of  each  part.  If  we 
distinguish  the  letters  referring  to  the  different  parts  by  accents, 
the  variation  in  the  energy  of  the  system  may  be  expressed  by 
Se'  -\-  Se"  -\-  etc.,  and  the  general  condition  of  equilibrium  requires 

that 

(Jt'+.f^f"  -h  etc,  ^  0  (14) 

for  all  variations  which  do  not  conflict  with  the  equations  of  condi- 
tion. These  equations  must  express  that  the  entropy  of  the  whole 
given  mass  does  not  vary,  nor  its  volume,  nor  the  total  quantities  of 
any  of  the  substances  ^Sj,  aS^j,  .  .  .  Sn-  We  will  suppose  that  there 
are  no  other  equations  of  condition.  It  will  then  be  necessary  for 
equilibrium  that 

i;  8r,'     ^  p' 6v'  H-///(Jm,'    -\-  i.i„' dm^J    . 
J^t"  67}"  - p"  6v"  -\-  1.1  ^"  dm ^"  +  lA^"  dm.J'  . 
-I-   etc.  ^  0 
for  any  values  of  the  variations  for  which 

6if  -f  67]"  +  67/"  4-  etc.  =  0, 
Sv'  -j-  6v"  +  6v"'  +  etc.  =  0, 


+  /'„'  6m.: 

+  yw„"  6m„ 

II 

(15) 

(16) 

(17) 

J.  W.  Gibbs — JEquilihrium  of  Heterogeneous  Substances.       119 

(18) 


drn^'  -\-  dm/'  +  dm/"  +  etc.  =  0,  ] 
dm./  +  dm/'  +  dm/"  +  etc.  =:  0, 


and     dm/  -\-  dm/'  -j-  dm/"  -\-  etc.  =  0. 
For  this  it  is  evidently  necessary  and  sufficient  that 

t'  =  t"  =zt"'z:i  etc.  (19) 

y  =y  =y'  —  etc.  (20) 

/Yj'  = //,"=///"=  etc.^ 

f.i/  —  H/'  z=  ^i/"  =  etc.  [  ^21) 

lA,!  z=  pi/'  =  fx/"  =.  etc.    J 

Equations  (19)  and  (20)  express  the  conditions  of  thermal  and 
mechanical  equilibrium,  viz.,  that  the  temperature  and  the  pressure 
must  be  constant  throughout  the  whole  mass.  In  equations  (21)  we 
have  the  conditions  characteristic  of  chemical  equilibrium.  If  we 
call  a  quantity  //„  as  defined  by  such  an  equation  as  (12),  the  potential 
for  the  substance  >S,  in  the  homogeneous  mass  considered,  these  con- 
ditions may  be  expressed  as  follows : 

The  potential  for  each  cotnponent  substance  must  be  constant 
throughout  the  lohole  mass. 

It  will  be  remembered  that  we  have  supposed  that  there  is  no 
restriction  upon  the  freedom  of  motion  or  combination  of  the  com- 
ponent substances,  and  that  each  is  an  actual  component  of  all  parts 
of  the  given  mass. 

The  state  of  the  whole  mass  will  be  completely  determined  (if  we 
regard  as  immaterial  the  position  and  form  of  the  various  homoge- 
neous parts  of  which  it  is  composed),  when  the  values  are  determined 
of  the  quautities  of  whicli  the  variations  occur  in  (15).  The  number 
of  these  quantities,  which  we  may  call  the  independent  variables,  is 
evidently  {n  -\-  2)  k,  k  denoting  the  number  of  homogeneous  parts 
into  which  the  whole  mass  is  divided.  All  the  quantities  which 
occur  in  (19),  (20),  (21),  are  functions  of  these  variables,  and  may  be 
regarded  as  known  functions,  if  the  energy  of  each  part  is  known  as 
a  function  of  its  entropy,  volume,  and  the  quantities  of  its  com- 
ponents. (See  eq.  (12).)  Therefore,  equations  (19),  (20),  (21),  may 
be  regarded  as  {v  -  1)  {n -\- 2)  independent  equations  between  the 
independent  variables.  The  volume  of  the  whole  mass  and  the  total 
quantities  of  the  various  substances  being  known  afford  n-\-  \  addi- 
tional equations.  If  we  also  know  the  total  energy  of  the  given 
mass,  or  its  total  entropy,  we  will  have  as  many  equations  as  there 
are  independent  variables. 


120      J^  W.  Gibbs — Equilibrmm  of  Heterogeneous  Substances. 

But  if  any  of  the  substances  S^,  S.^  .  .  .  S„  are  only  possible  com- 
ponents of  some  parts  of  the  given  mass,  the  variation  6m  of  the 
quantity  of  such  a  substance  in  such  a  part  cannot  have  a  negative 
value,  so  that  the  general  condition  of  equilibrium  (15)  does  not 
require  that  the  potential  for  that  substance  in  that  part  should  be 
equal  to  the  potential  for  the  same  substance  in  the  parts  of  which  it 
is  an  actual  component,  but  only  that  it  shall  not  be  less.  In  this 
case  instead  of  (21)  we  may  write 

for  all  parts  of  which  ^S'j  is  an  actual  component,  and 

for  all  parts  of  which  S^  is  a  possible  (but  not  actual)  com-  i 
ponent,  ' 

Ih  =  ^^2  y       (22) 

for  all  parts  of  which  iS'g  is  an  actual  component,  and 

for  all  parts  of  which  S2  is  a  possible  (but  not  actual)  com- 
ponent, 

etc., 

J/j,  M2,  etc.,  denoting  constants  of  which  the  value  is  only  deter- 
mined by  these  equations. 

If  we  now  suppose  that  the  components  (actual  or  possible)  of  the 
various  homogeneous  parts  of  the  given  mass  are  not  the  same,  the 
result  will  be  of  the  same  character  as  before,  provided  that  all  the 
different  components  are  indej^endeyit,  (i.  e.,  that  no  one  can  be  made 
out  of  the  others,)  so  that  the  total  quantity  of  each  component  is 
fixed.  The  general  condition  of  equilibi'ium  (15)  and  the  equations 
of  condition  (16),  (17),  (18)  Avill  require  no  change,  except  that,  if 
any  of  the  substances  S^ ,  S2  .  .  .  S„  is  not  a  component  (actual  or 
possible)  of  any  part,  the  term  fx  dm  for  that  substance  and  part  will 
be  wanting  in  the  former,  and  the  6m  in  the  latter.  This  will  require 
no  change  in  the  form  of  the  particular  conditions  of  equilibrium  as 
expressed  by  (19),  (20),  (22);  but  the  number  of  single  conditions 
contained  in'  (22)  is  of  course  less  than  if  all  the  component  sub- 
stances were  components  of  all  the  parts  Whenever,  therefore,  each 
of  the  different  homogeneous  parts  of  the  given  mass  may  be  regarded 
as  composed  of  some  or  of  all  of  the  same  set  of  substances,  no  one 
of  which  can  be  formed  out  of  the  others,  the  condition  which  (with 
equality  of  temperature  and  pressure]  is  necessary  and  sufficient  for 
equilibrium  between  the  different  parts  of  the  given  mass  may  be 
expressed  as  follows: 


J.  W.  Gihbs — Equilihrmm  of  Heterogeneous  Substances.       121 

The  potentUd  for  each  of  the  component  substances  must  luioe  a 
constant  value  in  all  parts  of  the  given  mass  of  iddch  that  substance 
is  an  actual  conxponeyit^  and  have  a  value  not  less  than  this  in  all 
parts  of  which  it  is  a  possible  componetit. 

The  number  of  equations  aftbrded  by  these  conditions,  after  elimina- 
tion of  J/j,  iT/g,  .  .  .  Jf„,  will  be  less  than  {n  +•  2)  (k  -  1)  by  the  num- 
ber of  terms  in  (15)  in  which  the  variation  of  the  form  dm  is  either 
necessarily  nothing  or  incapable  of  a  negative  value.  The  number  of 
variables  to  be  determined  is  diminished  by  the  same  number,  or,  if 
we  choose,  Ave  may  write  an  equaticm  of  the  form  m  —  0  for  each  of 
these  terms.  But  when  the  substance  is  a  possible  component  of  the 
part  concerned,  there  will  also  be  a  condition  (expressed  by  ^ )  to 
show  whether  the  supposition  that  the  substance  is  not  an  actual 
component  is  consistent  with  equilibrium. 

We  will  now  suppose  that  the  substances  S-^^,  8^,  .  .  .  iS„  are  not 
all  independent  of  each  other,  i.  e.,  that  some  of  them  can  be  formed 
out  of  others.  We  will  first  consider  a  very  simple  case.  Let  S^  be 
composed  of  S^  and  So  combined  in  the  ratio  of  a.  to  b,  S^  and  S2 
occurring  as  actual  components  in  some  parts  of  the  given  mass,  and 
/S'g  in  other  parts,  which  do  not  contain  S^  and  S2  as  separately 
A^ariable  components.  The  general  condition  of  equilibrium  will 
still  have  the  form  of  (15)  with  certain  of  the  terms  of  the  form 
/<  dm  omitted.     It  may  be  written  more  briefly  [(23) 

^{tSi/)  -  2{pdv)-^:::^{/.i,(hn^)-^2{/'2dm2)  ■  '  .-\-^^{Mn<^'n„)^0, 
the  sign  ^  denoting  suumiation  in  regard  to  the  difierent  parts  of 
the  given  mass.     But  instead  of  the  three  equations  of  condition, 

2  6m  1=0,     2"  dm2  =  0,     2  6m^  —  0,  (24) 

we  shall  have  the  two, 

2Sm,+^^2Sm,  =  0,] 

The  other  equations  of  condition, 

2  Sij  =  0,     :2  dv  =  0,     ^  Sm^  =  0,     etc.,  (26) 

will  remain  unchanged.  Now  as  all  values  of  the  variations  which 
satisfy  equations  (24)  will  also  satisfy  equations  (25),  it  is  evident 
that  all  the  particular  conditions  of  equilibrium  which  we  have 
already  deduced,  (19),  (20),  (22),  are  necessary  in  this  case  also. 
When  these  are  satisfied,  the  general  condition  (23)  reduces  to 
M,  2  6)n ,  -f  3f,  2  6m  2+  M^  2  6m 3^0.  (27) 

Trans.  Conn.  Acad.  16  October.  1875. 


;.  (25) 


122       J.  IF.  Glbhs — Equilihrium  of  Heterogeneous  Substances. 

For,  although  it  may  be  that  //j',  for  example,  is  greater  than  J/^, 
yet  it  can  only  be  so  when  the  following  Sin^'  is  incapable  of  a  nega- 
tive value.  Hence,  if  (27)  is  satisfied,  (23)  must  also  be.  Again,  if 
(23)  is  satisfied,  (27)  must  also  be  satisfied,  so  long  as  the  variation 
of  the  quantity  of  every  substance  has  the  value  0  in  all  the  parts  of 
which  it  is  not  an  actual  component.  But  as  this  limitation  does  not 
affect  the  range  of  the  possible  values  of  2  6m ^,  2  dni^,  and  2E  Sm^, 
it  may  be  disregarded.  Therefore  the  conditions  (23)  and  (27)  are 
entirely  equivalent,  when  (19),  (20),  (22)  are  satisfied.  Now,  by 
means  of  the  equations  of  condition  (25),  we  may  eliminate  2  6m^ 
and  ^6)712  from  (27),  which  becomes 

-  a  31  ^  2  6m  ^  —  hM^  2  6m^  +  {a  +  h)  M^:S  6m ^  ^  0,     (28) 
i.e.,  as  the  value  of  2  6m^  may  be  either  positive  or  negative, 

a  M^  ■\-bM2  —  {a-\-h)  M^,  (29) 

which  is  the  additional  condition  of  equilibrium  which  is  necessary 
in  this  case. 

The  relations  between  the  component  substances  may  be  less 
simple  than  in  this  case,  but  in  any  case  they  will  only  affect  the 
equations  of  condition,  and  these  may  always  be  found  without  diffi- 
culty, and  will  enable  us  to  eliminate  from  the  general  condition  of 
equilibrivim  as  many  variations  as  there  are  equations  of  condition, 
after  which  the  coefficients  of  the  remaining  variations  may  be  set 
equal  to  zero,  except  the  coefficients  of  variations  which  are  incapable 
of  negative  values,  which  coefficients  must  be  equal  to  or  greater 
than  zero.  It  will  be  easy  to  perform  these  operations  in  each  par- 
ticular case,  but  it  may  be  interesting  to  see  the  form  of  the  resultant 
equations  in  general. 

We  will  suppose  that  the  various  homogeneous  parts  are  considered 
as  having  in  all  n  comjjonents,  «Sj,  aS'^,  .  .  .  iS„,  and  that  there  is  no 
restriction  upon  their  freedom  of  motion  and  combination.  But  we 
Avill  so  far  limit  the  generality  of  the  problem  as  to  suppose  that 
each  of  these  components  is  an  actual  component  of  some  part  of 
the  given  mass.*  If  some  of  these  components  can  be  formed  out  of 
others,  all  such  relations  can  be  expressed  by  equations  such  as 

^^  ©a  +  P  S/,  +  etc.  =  n  e,  4-  A  i5,  +  etc.  (30) 

where  ©a,  <Si,  ®a,  etc.  denote  the  units  of  the  substances  /S„,  Si,,  S^,  etc., 

*  When  we  come  to  seek  the  conditions  of  equilibrium  relating  to  the  formation  of 
masses  unlike  any  previously  existing,  we  shall  take  up  de  novo  the  whole  problem 
of  the  equilibrium  of  heterogeneous  masses  enclosed  in  a  non-conducting  envelop, 
and  give  it  a  more  general  treatment,  which  will  be  free  from  this  limitation. 


J.  W.  Gibbs  —Equilibrium  of  Heterogeneous  Substances.      123 

(that  is,  of  certain  of  tlie  substances  »S'j,  ^S'^,  .  .  .  N,,,)  and  «-,  /:/,  h 
etc.  denote  numbers.  These  are  not,  it  will  be  observed,  equations 
between  abstract  quantities,  but  the  sign  =z  denotes  qualitative  as 
well  as  quantitative  equivalence.  We  will  suppose  that  there  are 
r  independent  equations  of  this  character.  The  equations  of  con- 
dition relating  to  the  component  substances  may  easily  be  derived 
from  these  equations,  but  it  will  not  be  necessary  to  consider  them 
particularly.  It  is  evident  that  they  will  be  satisfied  by  any  values 
of  the  variations  which  satisfy  equations  (18);  hence,  the  particular 
conditions  of  equilibrium  (19),  (20),  (22)  must  be  necessary  in  this 
case,  and,  if  these  are  satisfied,  the  general  equation  of  equilibrium 
(15)  or  (2.3)  will  reduce  to 

J/,  >;  dm  1  +  J/g  :^  drii^  .  .  .  -}-  31^2  6m„^  0.  (31) 

This  will  appear  from  the  same  considerations  which  were  used  in 
regard  to  equations  (2.3)  and  (27).  Now  it  is  evidently  possible  to 
give  to  2  Sm^,  2  dm,„  2  Snii.,  etc.  values  proportional  to  a,  fi,  —  ;<:, 
etc.  in  equation  (-30),  and  also  the  same  values  taken  negatively, 
making  2  dm  =^  0  in  each  of  the  other  terms ;  therefore 

aM^  +  pM,-\-  etc.  .  .  .  -  «  J/^.  -XM,^  etc.  ::^  0,         (32) 
or, 

a  M„  -\-  f-i  M,,  +  etc.  =  u  M^  -\- X  31^  +  etc.  (33) 

It  will  be  observed  that  this  equation  has  the  same  form  and  coeifi- 
cients  as  equation  (30),  JI  taking  the  place  of  ©.  It  is  evident  that 
there  must  be  a  similar  condition  of  equilibrium  for  every  one  of  the 
r  equations  of  which  (30)  is  an  example,  which  may  be  obtained  sim- 
ply by  changing  ©  in  these  equations  into  3f,  When  these  condi- 
tions are  satisfied,  (31)  will  be  satisfied  with  any  possible  values  of 
2  6m I,  2  Sni^,  ,  .  .  2  drii^.  For  no  values  of  these  quantities  are 
possible,  except  such  that  the  equation 

{2dm,)(S,-^{2dm.,)(B2  .  .   .  -\-{2dm,)e„=0  (84) 

after  the  substitution  of  these  values,  can  be  derived  from  the  r  equa- 
tions like  (30),  by  the  ordinary  processes  of  the  reduction  of  linear 
equations.  Therefore,  on  account  of  the  correspondence  between  (31) 
and  (34),  and  between  the  r  equations  like  (33)  and  the  r  equations 
like  (30),  the  conditions  obtained  by  giving  any  possible  values  to 
the  variations  in  (31)  may  also  be  derived  from  the  r  equations  like 
(33) ;  that  is,  the  condition  (31)  is  satisfied,  if  the  r  equations  like 
(33)  are  satisfied.  Therefore  the  r  equations  like  (33)  are  with 
(19),  (20),  and  (22)  the  equivalent  of  the  general  condition  (15) 
or  (23). 


124      J.  W.  Gibbs — Equilibrimn  of  Heterogeneous  ^Substances. 

For  determining  the  state  of  a  given  mass  when  in  equilibrium 
and  having  a  given  vohime  and  given  energy  or  entropy,  the  condi- 
tion of  equilibrium  affords  an  additional  equation  corresponding  to 
each  of  the  r  independent  relations  between  the  n  component  sub- 
stances. But  the  equations  which  express  our  knowledge  of  the 
matter  in  the  given  mass  will  be  correspondingly  diminished,  being 
n  —  r  m  number,  like  the  equations  of  condition  relating  to  the 
quantities  of  the  component  substances,  which  may  be  derived  from 
the  former  by  differentiation. 

Conditions  relating  to  the  possible  formation  of  Masses  Unlike  any 
Preiiiousli/  Existing. 
The  variations  which  we  have  hitherto  considered  do  not  embrace 
every  possible  infinitesimal  variation  in  the  state  of  the  given  mass, 
so  that  the  particular  conditions  already  formed,  although  always 
necessary  for  equilibrium  (when  there  are  no  other  equations  of  con- 
dition than  such  as  we  have  supposed),  are  not  always  sufficient. 
For,  besides  the  infinitesimal  variations  in  the  state  and  composition 
of  different  parts  of  the  given  mass,  infinitesimal  masses  may  be 
formed  entirely  different  in  state  and  composition  from  any  initially 
existing.  Such  parts  of  the  whole  mass  in  its  varied  state  as 
cannot  be  regarded  as  parts  of  the  initially  existing  mass  which 
have  been  infinitesimally  varied  in  state  and  composition,  we  will 
call  ne^o  parts.  These  will  necessai'ily  be  infinitely  small.  As  it  is 
more  convenient  to  regard  a  vacuum  as  a  limiting  case  of  extreme 
rarefaction  than  to  give  a  special  consideration  to  the  possible  for- 
mation of  empty  spaces  within  the  given  mass,  the  term  new  parts 
Avill  be  used  to  include  any  empty  spaces  which  may  be  formed, 
when  such  have  not  existed  initially.  We  will  use  De,  D?],  Dv,  Dm^, 
X>w?2,  .  .  .  Din^  to  denote  the  infinitesimal  enei'gy,  entropy,  and  vol- 
ume of  any  one  of  these  new  parts,  and  the  infinitesimal  quantities 
of  its  components.  The  component  substances  8^,8^,.  .  .  S„  must 
now  be  taken  to  include  not  only  the  independently  variable  com- 
ponents (actual  or  possible)  of  all  parts  of  the  given  mass  as  initially 
existing,  but  also  the  components  of  all  the  new  parts,  the  possible 
formation  of  which  we  have  to  consider.  The  character  S  will  be 
used  as  before  to  express  the  infinitesimal  variations  of  the  quantities 
relating  to  those  parts  which  are  only  infinitesimally  varied  in  state 
and  compc^sition,  and  which  for  distinction  we  will  call  orif/inal parts, 
including  under  this  term  the  empty  sj^aces,  if  such  exist  initially, 
within  the  envelop  bounding  the  system.  As  we  may  divide  the 
given  mass  into  as  many  parts  as  we  choose,  and    as  not  only  the 


J.  W.  Glhhs — Equilibrium  of  Heterogeneous  Substances.      125 

initial  bounclarie!^,  but  also  the  movements  of  these  bomidaries  during 
any  variation  in  the  state  of  the  system  are  arbitrary,  we  may  so 
define  the  parts  which  we  have  called  original,  that  we  may  consider 
them  as  initially  homogeneous  and  remaining  so,  and  as  initially  con- 
stituting the  whole  system. 

The  most  general  value  of  the  energy  of  the  whole  system  is 
evidently 

^68-\-^J)^,  (35) 

the  first  summation  relating  to  all  the  original  parts,  and  the  second 
to  all  the  new  parts.  (Throughout  the  discussion  of  this  problem,  the 
letter  6  or  D  following  ^  will  sufficiently  indicate  whether  the  sum- 
mation relates  to  the  original  or  to  the  new  parts.)  Therefore  the 
general  condition  of  equilibrium  is 

:^de-it-  :^6e^0,  (36) 

or,  if  w^e  substitute  the  value  of  de  taken  from  equation  (12),         [(37) 

^De^^{tSii)  -  2{2>dv)-\-2{i.i^dm^)-{.:£{iJ^6m.,) .  .  +^^(/v?w„)^  0. 

If  any  of  the  substances  S ^^  S^^  .  .  .  *S'„  can  be  formed  out  of  others, 
we  will  suppose,  as  before  (see  page  122),  that  such  relations  are 
expressed  by  equations  betw^een  the  units  of  the  different  substances. 
Let  these  be 

«j   ®1   -f    «2   ®2    •     •     •     +   ^nSn^  0  j 

^1  ®i  +  ^''s  ®3  •  •  •   +  ''■'n  ®n  =  0  >•  ^equations,  (38) 
etc.  ) 

The  equations  of  condition  will  be  (if  there  is  no  restriction  upon  the 
freedom  of  motion  and  composition  of  the  components) 

:E6t]  +  ^D)]=Q,  (39) 

:E6v  -\-2I>V:=iO,  (40) 

and  n  —  r  equations  of  the  form 

+  h„  (:S'  8m„  +  '2  Dm.„)  =  0  |' 
^^  {2  6m^  +2 Dm,)  +  z,  (2  Sm.,  +  2  Dm„)   .    .      ^   (41)* 

+  /„  {2  Sm„  +  2  Dm„)  =  0 
etc. 

*  In  regard  to  the  relation  between  the  coefficients  in  (41)  and  those  in  (38),  the 
reader  will  easily  convince  himself  that  the  coefficients  of  any  one  of  equations  (41) 
are  such  as  would  satisfy  all  the  equations  (38)  if  substituted  for  Sj,  .S'^,  .  .  .  S„;  and 
that  this  is  the  only  condition  which  these  coefficients  must  satisfy,  except  that  the 
.fi  _  r  sets  of  coefficients  shall  be  independent,  i.  e.,  shall  be  such  as  to  form  inde- 
pendent equations ;  and  that  this  relation  between  the  coefficients  of  the  two  sets  of 
equations  is  a  reciprocal  one. 


126      J.  TT.  (rihh$ — Equilibrium  of  ffetero(jfefieous  Substances. 

Xow,  using  Lagrange's  ''■method  of  multipliers,"*  we  will  sul)- 
tract  7'  {:^  6rf  +  I^  Dr>)  -P(2:'o\'  -\-  2:  I)r)  from  the  first  member 
of  the  general  condition  of  equilibrium  (^H),  7' and  P  being  constants 
of  which  the  value  is  as  vet  arbitrary.  We  might  proceed  in  the 
same  way  with  the  remaining  equations  of  condition,  but  we  may 
obtain  the  same  result  more  simply  in  another  way.  We  will  first 
observe  that 

+  (:i"  6m„  +  >:  Dm„)  S„  =  0,  (42) 
which  equation  would  hold  identically  for  any  possible  values  of  the 
quantities  in  the  parentheses,  if  for  r  of  the  letters  3j,  3^, .  .  .  ^„  were 
substituted  their  values  in  terms  of  the  others  as  derived  from  equa- 
tions (38).  (Although  2 ,,  Sg^ .  .  .  3n  do  not  represent  abstract  quanti- 
ties, yet  the  operations  necessary  for  the  reduction  of  linear  equations 
are  evidently  applicable  to  eqiuitious  (38).)  Therefore,  equation  (42) 
will  hold  true  if  for  3^,  Sg,  .  .  .  2„  we  substitute  n  numbers  which 
satisfy  equations  (38).  Let  3/,,  J/j,  .  .  .  3I„  be  such  numbers,  i.  e., 
let 

^»j  J/j  +  bo  3I2  .  .  .  +  b^  J/„  =  0,  '^  r  equations,  (43) 
etc.  ) 

then 

J/j  {:^Sm^^  :^Dm^)  +  M2  {2  6m2-h2Dm2)  .  .  . 

+  J/„  {:S  6m„  +  2i'  Din„)  =  0.        (44) 

This  expression,  in  which  the  values  of  «  —  r  of  the  constants  J/,,  J/g? 
.  .  .  JI„  are  still  arbitrary,  we  will  also  subtract  from  the  first  mem- 
ber of  the  general  condition  of  equilibrium  (37),  which  will  then 
become 

2D€+  2  {t  d>;)  -  :^  (/)  dv)  -{-  2  (;/ ,6m,)  .  .  +  2:  (//„  6m„) 

-  T2  d//  +  1^2  6v     -  M,  2  6m ,  .  .  .  +  J/'„  v  (^m„ 

-  T2Dr^-\-F:SDv   -3/,  :2Dm,  ..  .  -J/„  >Z)w„^0.    (45) 

That  is,  having  assigned  to  T,  P,  Jl,,  JJ^,  .  .  .  3/„  any  values  con- 
sistent with  (43),  we  may  assert  that  it  is  necessaiy  and  sufficient  for 
equilibrium  that  (45)  shall  hold  true  for  any  variations  in  the  state 
of  the  system  consistent  with  the  equations  of  condition  (39),  (40), 
(41).  But  it  will  always  be  possible,  in  case  of  equilibrium,  to  assign 
such  values  to  T,  P,  M,^  Jf^, .  .  M^,  without  violating  equations  (43), 

*  On  account  of  the  sign  ^  in  (37),  and  because  some  of  the  variations  are  incapable 
of  negative  values,  the  successive  steps  in  the  reasoning  vriU  be  developed  at  greater 
length  than  would  be  otherwise  necessary. 


,1.    \V.   Oihbs — Kijidlihriidii  of  n>fii'i><inivi>i(H  Su/isfa )/<•,. t.       127 

tli:it  (4">)  shall  lioM  Inic  tor  all  va^iati^•n^  in  ihc  slate  of  the  system 
ami  ill  tlie  <]uaiititi('s  ot'  tlie  various  Hulistanees  eomposiiitj  it,  even 
tlioui;;li  these  v;iriati<>iis  an-  not  consistent  with  the  e(|nations  of  con- 
dition (39),  (40),  (41),  For,  when  it  is  not  |>ossil)le  \i,  dn  this,  it 
must  be  possil)le  by  a|i|)lyin«;  (45)  to  variations  in  the  HyKtcrn  not 
necessarily  restricletl  by  the  etjuations  of  condition  (-M*),  (40),  (41)  to 
obtain  conditions  in  re«:;ard  to  7\  /\  .l/,,  .1/,,,  .  .  .  M„,  Home  of 
which  will  be  inconsistent  with  others  or  with  c(|nalions  (4:i).  'I'liese 
conditions  we  will  repreBoiit  by 

-1=0,     7?^  0,     etc.,  (JC.) 

.1,  />,  etc.  beint;  lineai-  functions  of  7',  /',  .1/,,  .1/.,,  .  .  .1/,.  Then  it 
will  be  possible  to  deduce  fioni  these  conditions  a  sinj^le  condition  of 
the  ft)rin 

n  A  +  /i  n  +  etc.  ^0,  (47) 

(K,  fi,  v\c.  beini;  positive  constants,  which  cannot  hold  true  consist- 
ently with  ecpuvtions  (43).  Hut  it  is  evident  from  the  form  of  (47) 
tliat,  like  any  of  the  eontlitions  (40),  it  couhl  have  been  obtained 
directly  from  (4'))  by  applying  this  formula  to  a  certain  chanj.(e  in 
tlie  system  (|)erha])S  not  restrictcil  by  the  ecpiations  ot  condition  (30), 
(40),  (41)).  Now  as  (47)  cannot  hold  true  consistently  with  eqs.  (43), 
it  is  evident,  in  the  tirst  place,  that  it  cannot  contain  7'or  /*,  there- 
fore in  the  diange  in  the  system  just  mentioneil  (for  which  (45) 
reduces  to  (47)) 

2^6>/  +  :::  J>/f=^\  and  2:  O/- -f  2:' />>/"  =  0, 
so  that  the  equations  of  condition  (39)  aiid  (40)  are  satisfied.  Again, 
for  the  same  reason,  the  homogeneous  function  of  the  first  degree  of 
JAj,  J/o,  .  .  .  J/„  in  (47)  must  be  one  of  which  the  value  is  fixed  by 
eqs.  (43).  l)ut  the  value  thus  fixed  can  only  be  zero,  as  is  evident 
from  the  form  of  these  equations.     Therefore 

( >■  ()■/// ,  +  :^'  it/n , )  J/,  +  ( :i"  6)n ,  +  ::i"  Um^ )  j/,  .  .  . 

+  ( ^"  (h,}„  +  :i  lJni„)  J/„  —  0         (4 8) 

for  any  values  of  ^/^,  M^  .  .  .  J/„  which  satisfy  eqs.  (43),  and 
theretore 

(I^'fJ///,  +  >Z>///i)  3j+  (:^'(J;«2  + ^"^'"2)  2j    •    •    • 

+  (  >'  d'i/,„  +  >■  Jjjn„)  2„  =  0  (49) 

for  any  numerical  values  of  2^^,  Z2,  .  •  .  3„  wdiich  satisfy  e«is,  (3ft). 
This  equation  (40)  will  therefore  hold  true,  if  for  r  of  the  letters 
3,2.,..  3„  we  substitute  their  values  in  terms  of  the  others 
taken  from  eqs.   (38),  and  therefore  it  will  hold  true  when  we  use 


128      J,  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 

<Sj,  ®2,  •  •  •  ©n,  as  before,  to  denote  the  units  of  the  various  com- 
ponents. Thus  understood,  the  equation  expresses  that  the  vahies 
of  the  quantities  in  the  parentheses  are  such  as  are  consistent  with 
the  equations  of  condition  (41).  The  change  in  the  system,  there- 
fore, which  we  are  considering,  is  not  one  which  violates  any  of  the 
equations  of  condition,  and  as  (45)  does  not  hold  true  for  this  change, 
and  for  all  values  of  2\  P,  J/^,  J/2,  •  •  •  ^^A  which  are  consistent 
with  eqs.  (43),  the  state  of  the  system  cannot  be  one  of  equilibrium. 
Therefore  it  is  necessary,  and  it  is  evidently  sufficient  for  equilibrium, 
that  it  shall  be  possible  to  assign  to  2\  P,  31^,  31^,  .  .  .  M„  such  values, 
consistent  with  eqs.  (43),  that  the  condition  (45)  shall  hold  true  for 
any  change  in  the  system  irrespective  of  the  equations  of  condition 
(39),  (40),  (41). 

For  this  it  is  necessary  and  sufficient  that 

t=2\        p  =  P,  (50) 

for  each  of  the  original  parts  as  previously  defined,  and  that 

Be  -  TDi]^PDr  -  J/,  X*;//,  -  M^Dm^  ...  -  3I,,Dm„^  0,  (52) 

for  each  of  the  7iew  parts  as  previously  defined.  If  to  these  condi- 
tions we  add  equations  (43),  we  may  treat  1\  P,  J/^,  J/g,  .  .  .  J/„ 
simply  as  unknown  quantities  to  be  eliminated. 

In  regard  to  conditions  (51),  it  will  be  observed  that  if  a  sub- 
stance, 6' J,  is  an  actual  component  of  the  part  of  the  given  mass 
distinguished  by  a  single  ac<^ent,  dtn^'  may  be  either  positive  or 
negative,  and  we  shall  have  fi^'  =  M^  ;  but  if  S^  is  only  a  possible 
component  of  that  part,  (Sm^'  will  be  incapable  of  a  negative  value, 
and  we  will  have  /^^'^  M^. 

The  formula^  (S*^)-  (51),  ^^^^^  (43)  express  the  same  particular  con- 
ditions of  equilibrium  which  we  have  before  obtained  by  a  less  gen- 
eral process.  It  remains  to  discuss  (52).  This  formula  must  hold 
true  of  any  infinitesimal  mass  in  the  system  in  its  varied  state  which 
is  not  approximately  homogeneous  with  any  of  the  surrounding 
masses,  the  expressions  i>£,  J9//,  i>y.  Dm  ^,  J)in2,  .  .  .  Dm„  denoting 
the  energy,  entropy,  and  volume  of  this  infinitesimal  mass,  and  the 
quantities  of  the  substances  S^,  S.y,  .  .  .  *S'„  which  we  regard  as  com- 
posing it,  (not  necessarily  as  independently  variable  components). 
If  there  is  more  tlian  one  way  in  which  this  mass  may  be  considered 
as  composed  of  these  substances,  we  may  choose  whichever  is  most 
convenient.  Indeed  it  follows  directly  from  the  relations  existing 
between  J/j,  J/g,  .  .  .  and  J/„  that  the  result  Avould  be  the  same  in 


./  W.  Gibbs — Equilibriuiu  of  Heterogeneous  /Substances.      rJ9 

any  case.  Now,  if  we  assume  tliat  the  values  of  i>f,  />;/,  JDo,  Drn^, 
Dm.^,  .  .  .  Din„  are  proportional  to  the  values  of  f,  //,  v,  m,,  jh.^,  .  .  . 
m„  for  any  large  homogeneous  mass  of  similar  composition,  and  of 
the  same  temperature  and  pressure,  the  condition  is  equivalent  to 
this,  that 

€  -  T?^  +  Pv  -  3Ij  m^  -3I2  in^  ...  -  iT/„m„  ^  0  (53) 

for  any  large  homogeneous  body  which  can  be  formed  out  of  the 
substances  aS'j,  S2  .  .  .  S„. 

But  the  validity  of  this  last  transformation  cannot  be  admitted 
without  considerable  limitation.  It  is  assumed  that  the  relation 
between  the  energy,  entropy,  volume,  and  the  quantities  of  the  dif- 
ferent components  of  a  very  small  mass  surrounded  by  substances 
of  diiferent  composition  and  state  is  the  same  as  if  the  mass  in  ques- 
tion formed  a  jaart  of  a  large  homogeneous  body.  We  started, 
indeed,  with  the  assumption  that  we  might  neglect  the  part  of  the 
energy,  etc.,  depending  upon  the  surfaces  separating  heterogeneous 
masses.  Now,  in  many  cases,  and  for  many  purposes,  as,  in  general, 
when  the  masses  are  large,  such  an  assumption  is  quite  legitimate, 
but  in  the  case  of  these  masses  which  are  formed  within  or  among 
substances  of  different  nature  or  state,  and  which  at  their  first  forma- 
tion mi;st  be  infinitely  small,  the  same  assumption  is  evidently 
entirely  inadmissible,  as  the  siirfaces  must  be  regarded  as  infinitely 
large  in  proportion  to  the  masses.  We  shall  see  hereafter  what 
modifications  are  necessary  in  our  formula  in  order  to  include  the 
parts  of  the  energy,  etc.,  which  are  due  to  the  surfaces,  but  this  will 
be  on  the  assinnption,  which  is  usual  in  the  theory  of  capillarity, 
that  the  radius  of  curvature  of  the  surfaces  is  large  in  proportion  to 
the  radius  of  sensible  molecular  action,  and  also  to  the  thickness  of 
the  lamina  of  matter  at  the  surface  which  is  not  (sensibly)  homoge- 
neous in  all  respects  with  either  of  the  masses  which  it  separates. 
But  although  the  formula?  thus  modified  will  apply  with  sensible 
accuracy  to  masses  (occurring  within  masses  of  a  diftei'ent  nature) 
much  smaller  than  if  the  terms  relating  to  the  surfaces  were  omitted, 
yet  their  failure  when  applied  to  masses  infinitely  small  in  all  their 
dimensions  is  not  less  absolute. 

Considerations  like  the  foregoing  might  render  doubtful  the  validity 
even  of  (52)  as  the  necessary  and  sufiicient  condition  of  equilibrium 
in  regard  to  the  formation  of  masses  not  approximately  homogeneous 
with  those  previously  existing,  when  the  conditions  of  equilibrium 
between  the  latter  are  satisfied,  unless  it  is  shown  that  in  establishing 
this  formula  there  have  been  no  quantities  neglected  relating  to  the 

Trans.  Conn.  Acad.,  Vol.  III.  17  October,  1875. 


130      ./.  IK  (xibbs — EnullibrlaiH  of  Heteroaeneous  Substances. 

mutual  actiou  of  the  new  and  the  original  parts,  which  can  aftect  the 
result.  It  will  be  easy  to  give  such  a  meaning  to  the  expressions 
7>f,  Di},  DiJ,  D„i^,  Dni^,  .  .  .  Dm„  that  this  shall  be  evidently  the 
case.  It  will  be  observed  that  the  quantities  represented  by  these 
expressions  have  not  been  pei-fectly  defined.  In  the  first  place,  we 
have  no  right  to  assume  the  existence  of  any  surface  of  absolute  dis- 
continuity to  divide  the  new  parts  from  the  original,  so  that  the 
position  given  to  the  dividing  surface  is  to  a  certain  extent  arbitrary. 
Even  if  the  surface  separating  the  masses  were  determined,  the 
energy  to  be  attributed  to  the  masses  separated  would  be  partly 
arl)itrary,  since  a  part  of  the  total  energy  depends  upon  the  mutual 
action  of  the  two  masses.  We  ought  perhaps  to  consider  the  case 
the  same  in  regard  to  the  entropy,  although  the  entropy  of  a  system 
never  depends  upon  the  mutual  relations  of  parts  at  sensible  dis- 
tances from  one  another.  Now  the  condition  (52)  will  be  valid  if 
the  quantities  Df,  7>//,  l>f,  I)m^,  Dm.-,  .  .  .  I))u„  are  so  defined  that 
none  of  the  assmuptious  which  have  been  made,  tacitly  or  otherwise, 
relating  to  the  formation  of  these  new  parts,  shall  be  violated.  These 
assumptions  are  the  following: — that  the  relation  between  the  varia- 
tions of  the  energy,  entropy,  volume,  etc.,  of  any  of  the  original  parts 
is  not  aifected  by  the  vicinity  of  the  new  parts;  and  that  the  energy, 
entropy,  volume,  etc.,  of  the  system  in  its  varied  state  are  correctly 
represented  by  the  sums  of  the  energies,  entropies,  volumes,  etc.,  of 
the  various  parts  (original  and  new),  so  far  at  least  as  any  of  these 
quantities  are  determined  or  aftected  by  the  formation  of  the  new 
parts.  We  will  suppose  Z>f,  Dij,  iJv,  Dm ^,  Dni^  .  .  .  Dm,,  to  be 
so  defined  that  these  conditions  shall  not  be  violated.  This  may  be 
done  in  various  ways.  We  may  suppose  that  the  jjosition  of  the 
surfaces  separating  the  new  and  the  original  parts  has  been  fixed  in 
any  suitable  way.  Tiiis  Avill  detej-mine  the  space  and  the  matter 
belonging  to  the  parts  separated.  If  this  does  not  determine  the 
division  of  the  entropy,  we  may  suppose  this  determined  in  any  suit- 
able arbitrary  way.  Thus  we  may  suppose  the  total  energy  in  and 
about  any  ne\v  part  to  be  so  distributed  that  equation  (12)  as  applied 
to  the  original  parts  shall  not  be  violated  by  the  formation  of  the 
new  parts.  Or,  it  may  seem  more  simple  to  suppose  that  the 
imaginary  surface  which  divides  any  new  part  from  the  original  is 
so  placed  as  to  include  all  the  matter  which  is  affected  by  the 
vicinity  of  the  new  formation,  so  that  the  part  or  parts  which  we 
regard  as  original  may  be  left  homogeneous  in  the  strictest  sense, 
including  uniform  dentilties  of  eneryij  and  entropy.,  up  to  the  very 


J.  W.  (Tihhs—I'JqKMlhriviii  of  Ueterof/eneoKS  Substances.      131 

bounding  surface.  The  homogeneity  of  the  new  parts  is  of  no  con- 
sequence, as  we  have  made  no  assumption  in  that  respect.  It  may 
l)e  doubtful  whether  we  can  consider  the  new  parts,  as  thus  hounded, 
to  be  infinitely  small  even  in  tlieir  earliest  stages  of  development.  But 
if  they  are  not  infinitely  small,  the  only  way  in  which  this  can  aftect 
the  validity  of  our  formuhe  will  be  that  in  virtue  of  the  equations  of 
condition,  i.  e.,  in  virtue  of  the  evident  necessities  of  the  case,  finite 
variations  of  the  energy,  entropy,  volume,  etc.,  of  the  original  parts 
will  be  caused,  to  which  it  might  seem  that  equation  (12)  would  not 
apply.  But  if  the  nature  and  state  of  the  mass  be  not  varied,  equa- 
tion (12)  will  hold  true  of  finite  dift'erences.  (This  appears  at  once, 
if  we  integrate  the  equation  under  the  above  limitation.)  Hence, 
the  equation  will  hold  true  for  finite  diiferences,  provided  that  the 
nature  and  state  of  the  mass  be  infinitely  little  varied.  For  the  dif- 
ferences may  be  considered  as  made  up  of  two  parts,  of  which  the 
first  are  for  a  constant  nature  and  state  of  the  mass,  and  the  second 
are  infinitely  small.  We  may  therefore  regard  the  new  parts  to  be 
bounded  as  supposed  without  prejudice  to  the  validity  of  any  of  our 
results. 

The  condition  (52)  understood  in  either  of  these  ways  (or  in 
others  which  will  suggest  themselves  to  the  reader)  will  have  a  per- 
fectly definite  meaning,  and  will  be  valid  as  the  necessary  and  sufii- 
cient  condition  of  equilibi-ium  in  regard  to  the  formation  of  new 
parts,  when  the  conditions  of  equilibrium  in  regard  to  tlie  original 
parts,  (50),  (51),  and  (43),  are  satisfied. 

In  regard  tf)  the  condition  (53),  it  may  be  shown  that  with  (50), 
(51),  and  (43)  it  is  always  suflicient  for  equilibrium.  To  prove  this, 
it  is  only  necessary  to  show  that  when  (50),  (51),  and  (43)  are  satis- 
fied, and  (52)  is  not,  (53)  will  also  not  be  satisfied. 

We  will  first  observe  that  an  expression  of  the  form 

_  e+  Tij-  Pv^  J/,  m^  +  J/,  "^2  •  •  •   +  -K  i'^n  (54) 

denotes  the  work  olnainable  V)y  the  formation  (by  a  reversible  pro- 
cess) of  a  body  of  which  f,  ;/,  v,  m^,  in.^,  .  .  .  m„  are  the  energy, 
entropy,  volume,  and  the  quantities  of  the  components,  within  a 
medium  having  the  pressure  P,  the  temperature  7]  and  tlie  potentials 
31  ,  J/2,  .  .  .  M„.  (The  medium  is  supposed  so  large  that  its  prop- 
erties are  not  sensibly  altered  in  any  part  by  the  formation  of  the 
body.)  For  f  is  the  energy  of  the  body  formed,  and  the  remaining 
terms  represent  (as  may  be  seen  by  applying  equation  (12)  to  the 
medium)   the  decrease   of  the  energy  of  the  medium,  if,   after  the 


1:^2      J.  TF.  Gibbs—Eqailibviiim,  of  Heterogeneoiis  Svbstances. 

formation  of  the  body,  the  joint  entropy  of  the  medium  and  the 
hody,  their  joint  volumes  and  joint  quantities  of  matter,  were  the 
same  as  the  entropy,  etc.,  of  the  medium  before  the  formation  of  the 
body.  Tliis  consideration  may  convince  us  that  for  any  given  finite 
values  of  v  and  of  T,  P,  31^ ,  etc.  this  expression  cannot  be  infinite 
when  f,  //,  m,,  etc.  are  determined  by  any  real  body,  whether  homo- 
geneous or  not,  (but  of  the  given  volume),  even  when  T,  P,  3/j,  etc. 
do  not  represent  the  values  of  the  temperature,  pressure,  and  poten- 
tials of  any  real  substance.  (If  the  substances  *S',,  /Sg,  .  .  .  S„  are 
all  actual  components  of  any  homogeneous  part  of  the  system  of 
which  the  equilibrium  is  discussed,  that  part  will  aiford  an  example 
of  a  body  having  the  temperature,  pressure,  and  potentials  of  the 
medium  supposed.) 

Now  by  integrating  equation  (12)  on  the  supposition  that  the 
nature  and  state  of  the  mass  considered  i-emain  unchanged,  we  obtain 
the  equation 

which  will  hold  true  of  any  homogeneous  mass  whatever.     Therefore 
for  any  one  of  the  original  parts,  by  (50)  and  (51), 

f  -  T)]-\-Pv-M^  m J  -  J/2  »«2  •  •  •  —  ^^n ^''„  =  0.  (56) 
If  the  condition  (52)  is  not  satisfied  in  regard  to  all  possible  new 
parts,  let  JVhe  a  new  part  occurring  in  an  original  part  O,  for  which 
the  condition  is  not  satisfied.  It  is  evident  that  the  value  of  the 
expression 

s—Ti]  +  Pv  -  M^  m^  —  31^  m^   .  .  .   —3f„m„  (57) 

applied  to  a  mass  like  0  including  some  very  small  masses  like  JV, 
will  be  negative,  and  will  decrease  if  the  number  of  these  masses  like 
JV  is  increased,  until  there  remains  within  the  whole  mass  no  portion 
of  any  sensible  size  without  these  masses  like  iV,  which,  it  will  be 
remembered,  have  no  sensible  size.  But  it  cannot  decrease  without 
limit,  as  the  value  of  (54)  cannot  become  infinite.  Now  we  need  not 
inquire  whether  the  least  value  of  (57)  (for  constant  values  of  T,  P, 
M^,  J/g*  •  •  •  -^^")  would  be  obtained  by  excluding  entirely  the 
mass  like  0,  and  filling  the  whole  space  considered  with  masses  like 
iV,  or  whether  a  certain  mixture  would  give  a  smaller  value, — it  is 
certain  that  the  least  possible  value  of  (57)  per  unit  of  volume,  and 
that  a  negative  value,  will  be  realized  by  a  mass  having  a  certain 
homogeneity.  If  the  new  part  iVfor  which  the  condition  (52)  is  not 
satisfied  occurs  between  two  diflferent  original  parts  0'  and  6>",  the 
aigument  need    not  be  essentially   varied.     We    may   consider  the 


J.  W.  Gihbs — Eqxiilihrium  of  Heterogeneous  Substances.       133 

value  of  (57).  for  u  body  consisting  of  masses  like  O'  and  0"  sepa- 
rated by  a  lamina  i\^.  This  value  may  be  decreased  by^increasing 
the  extent  of  this  lamina,  which  may  be  done  within  a  given  volume 
by  giving  it  a  convoluted  form ;  and  it  will  be  evident,  as  before, 
that  the  least  possible  value  of  (57)  will  be  for  a  homogeneous  mass, 
and  that  the  value  will  be  negative.  And  such  a  mass  will  be  not 
merely  an  ideal  combination,  but  a  body  capable  of  existing,  for  as  the 
expression  (57)  has  for  this  mass  in  the  state  considered  its  least  pos- 
sible value  per  unit  of  volume,  the  energy  of  the  mass  included  in  a 
unit  of  volume  is  the  least  possible  for  the  same  matter  with  the 
same  entropy  and  volume, — hence,  if  confined  in  a  non-conducting 
vessel,  it  will  be  in  a  state  of  not  unstable  equilibrium.  Therefore 
when  (50),  (51),  and  (43)  are  satisfied,  if  the  condition  (52)  is  not  sat- 
isfied in  regard  to  all  possible  new  parts,  there  will  be  some  homo- 
geneous body  which  can  be  formed  out  of  the  substances  aS'^,  ^Sg,  .  .  . 
S„  which  will  not  satisfy  condition  (53). 

Therefore,  if  the  initially  existing  masses  satisfy  the  conditions 
(50),  (51),  and  (43),  and  condition  (53)  is  satisfied  by  every  homoge- 
neous body  which  can  be  formed  out  of  the  given  matter,  there  will 
be  equilibrium. 

On  the  other  hand,  (53)  is  not  a  necessary  condition  of  equilibrium. 
For  we  may  easily  conceive  that  the  condition  (52)  shall  hold  true 
(for  any  very  small  formations  within  or  between  any  of  the  given 
masses),  while  the  condition  (53)  is  not  satisfied  (for  all  large  masses 
formed  of  the  given  matter),  and  experience  shows  that  this  is  very 
often  the  case.  Supersaturated  solutions,  superheated  water,  etc., 
are  familiar  examples.  Such  an  equilibrium  will,  however,  be  practi- 
cally unstalde.  By  this  is  meant  that,  although,  strictly  speaking, 
an  infinitely  small  disturbance  or  change  may  not  be  suflicient  to 
destroy  the  equilibrium,  yet  a  very  small  change  in  the  initial  state, 
perhaps  a  circumstance  which  entirely  escapes  our  powers  of  percep- 
tion, will  be  sufficient  to  do  so.  The  presence  of  a  small  portion  of 
the  substance  for  which  tlie  condition  (53)  does  not  hold  true,  is  suffi- 
cient to  produce  this  result,  when  this  substance  forms  a  variable 
component  of  the  original  homogeneous  masses.  In  other  cases, 
when,  if  the  new  substances  are  formed  at  all,  different  kinds  must  be 
formed  simultaneously,  the  initial  presence  of  the  different  kinds, 
and  that  in  immediate  proximity,  may  be  necessary. 

It  will  be  observed,  that  from  (56)  and  (53)  we  can  at  once  obtain 
(50)  and  (51),  viz.,  by  applying  (53)  to  bodies  differing  infinitely 
little  from  the  various  homogeneous  ])arts  of  the  given  mass.     There- 


134      ./  TK  fribbs — Equilibrium  of  Heterogeneous  Substances. 

fore,  the  condition  (56)  (relating  to  the  various  homogeneous  parts 
of  the  given  mass)  and  (53)  (relating  to  any  bodies  which  can  be 
formed  of  the  given  matter)  with  (43)  are  always  sufficient  for  equi- 
librium, and  always  necessary  for  an  equilibrium  which  shall  be 
practically  stable.  And,  if  we  choose,  we  may  get  rid  of  limitation 
in  regard  to  equations  (43).  For,  if  we  compare  these  equations 
with  (38),  it  is  easy  to  see  that  it  is  always  immaterial,  in  applying 
the  tests  (56)  and  (53)  to  any  body,  how  we  consider  it  to  be  com- 
posed. Hence,  in  applying  these  tests,  we  may  consider  all  bodies  to 
be  composed  of  the  ultimate  components  of  the  given  mass.  Then 
the  terms  in  (56)  and  (53)  which  relate  to  other  components  than 
these  will  vanish,  and  we  need  not  regard  the  equations  (43).  Such 
of  the  constants  M ^,  M.^  .  .  .  3I„  as  relate  to  the  ultimate  compo 
ponents,  may  be  regarded,  like  T  and  P,  as  unknown  quantities  sub- 
ject only  to  the  conditions  (56)  and  (53). 

These  two  conditions,  which  are  sufficient  for  equilibrium  and 
necessary  for  a  practically  stable  equilibrium,  may  be  united  in  one, 
viz.,  (if  we  choose  the  ultimate  components  of  the  given  mass  for 
the  component  substances  to  which  Wj,  w-g,  .  .  .  m^  relate)  that  it 
shall  be  possible  to  give  such  values  to  the  constants  T,  P,  J/j,  J/2? 
.  .  .  M^  in  the  expi'ession  (o*?)  that  the  value  of  the  expression  for 
each  of  the  homogeneous  parts  of  the  mass  in  question  shall  be  as 
small  as  for  any  body  whatever  made  of  the  same  components. 

Effect  of  Solidity  of  any  Part  of  the  given  Mass. 

If  any  of  the  homogeneous  masses  of  which  the  equilibrium  is  in 
question  are  solid,  it  will  evidently  be  proper  to  treat  the  proportion 
of  their  components  as  invariable  in  the  application  of  the  criterion 
of  equilibrium,  even  in  the  case  of  compounds  of  variable  proportions., 
i.  e.,  even  when  bodies  can  exist  which  are  compounded  in  pro- 
portions infinitesimally  varied  from  those  of  the  solids  considered. 
(Those  solids  which  are  capable  of  absorbing  fluids  form  of  course  an 
exception,  so  far  as  their  fluid  components  are  concerned.)  It  is  true 
that  a  solid  may  be  increased  by  the  formation  of  new  solid  matter 
on  the  surface  where  it  meets  a  fluid,  which  is  not  homogeneous  with 
the  previously  existing  solid,  but  such  a  deposit  will  properly  be 
treated  as  a  distinct  part  of  the  system,  (viz.,  as  one  of  the  parts 
which  we  have  called  new).  Yet  it  is  worthy  of  notice  that  if  a  homo- 
geneous solid  which  is  a  compound  of  variable  proportions  is  in 
contact  and  equilibrium  with  a  fluid,  and  the  actual  components  of 
the  solid  (considered  as  of  variable  composition)  are  also  actual  com- 


J.  W.  Gihhs—Eqailibrli(m  of  Heterogeneous  Substances.      135 

poiients  of  the  fluid,  and  tlie  condition  (53)  is  satisfied  in  regard  to 
all  bodies  which  can  l)e  formed  out  of  the  actual  components  of  the 
fluid,  (which  will  ahvaj-s  be  the  case  unless  the  fluid  is  practically 
unstable,)  all  the  conditions  will  hold  true  of  the  solid,  which  would 
be  necessary  for  equilibrium  if  it  were  fluid. 

This  follows  directly  from  the  principles  stated  on  the  preceding 
pages.  For  in  this  case  the  value  of  (57)  will  be  zero  as  determined 
either  for  the  solid  or  for  the  fluid  considered  with  reference  to  their 
ultimate  components,  and  will  not  be  negative  for  any  body  Avhatever 
which  can  be  formed  of  these  components;  and  these  conditions  are 
sufficient  for  equilibrium  independently  of  the  solidity  of  one  of  the 
masses.  Yet  the  point  is  perhaps  of  sufficient  importance  to  demand 
a  more  detailed  consideration. 

Let  xS„  .  .  .  >%  be  the  actual  components  of  the  solid,  and  aS'^,  .  .  .  S,, 
its  possible  components  (which  occur  as  actual  components  in  the 
fluid);  then,  considering  the  proportion  of  the  components  of  the 
solid  as  variable,  we  shall  have  for  this  body  by  equation  (12) 

cW  =  t  d)j  -  ^y  civ'  -f-  //,/  dm  J  .  .  .  H-  //;  dm.J 

+  pi/dm^'  .  .  .  i-jutdn^.  (58) 

By  this  equation  the  potentials  j.ij  .  .  .  /u^.'  are  perfectly  defined. 
But  the  difierentials  dm„'  .  .  .  dmi.',  considered  as  independent,  evi- 
dently express  variations  w^hich  are  not  possible  in  the  sense  required 
in  the  criterion  of  equilibrium.  We  might,  however,  introduce  them 
into  the  genei-al  condition  of  equilibrium,  if  we  should  express  the 
dependence  between  them  by  the  j^roper  equations  of  condition. 
But  it  will  be  more  in  accordance  with  our  method  hitherto,  if  we 
consider  the  solid  to  have  only  a  single  independently  variable  com- 
ponent S^,  of  Avhich  the  nature  is  represented  by  the  solid  itself.  We 
may  then  write 

6e'=t'  dif  —  p'  dv'  -f-  jjj  6niJ.  (59) 

In  regard  to  the  relation  of  the  potential  /^/  to  the  potentials  occur- 
ring in  equation  (58)  it  will  be  observed,  that  as  we  have  by  integra- 
tion of  (58)  and  (59) 

a'  =:  t'  if  -  p'  v'  -\-  /.(„'  mj  .   .  .    +  pij  nij,  (60) 

and  e'  =  t'  ?/  —  p'  v'  +  /jJ  mj ;  (61) 

therefore  /.tj  jt/J  =  /.tj  mj  .  .  .    -\-f.i,'m,'.  (62) 

Now,  if  the  fluid  has  besides  S^,  .  .  .  S,,  and  *S/,  .  .  .  S^.  the  actual 
components  S/  .  .  .   /S„,  we  may  write  for  the  fluid 


130      J  W.  Gibbs — Eqailibriain  of  Heterogeneous  Substances. 

+  11,"  Sm,"  .  .  .  +  /.It"  6m,r-{-pi/'  dm/'  .  .  .    + //„"  f^?«„",     (63) 
and  as  by  suppusition 

nij  ®^  =  mj  ©„...+  »'*</'  ®.v  (6*) 

equations  (43),  (oO),  and  (51)  will  give  in  this  ease  on  elimination  of 
the  constants  T,  P,  etc., 

t'=:t",     p'=p",  (65) 

and 

mj  M.' =  '".,'  I-'.."  ■  •  •    +w^;  //,/'•  (66) 

Equations  (65)  and  (66)  may  be  regarded  as  expressing  the  condi- 
tions of  equilibrium  between  the  solid  and  the  fluid.  The  last  con- 
dition may  also,  in  virtue  of  (62),  be  expressed  by  the  equation 

w,,'//,,'  .  .  .  -j-n,;  /.i;  =  mj  /j„"  .  .  .  +';/*,>;'.  (67) 

But  if  condition  (53)  holds  true  of  all  bodies  which  can  be  formed 

of  «S'„  .  .  .  S^,  S,„  .  .  .   iSi;  S,  .  .  .  /8„,  we  may  write  for  all  such  bodies 

£  —  t"  ?/-\-p"  V  —  //„"  m„ ...  —  //,/'  m„  —  //;,"  nh 

.  .  .  — /V'w'i-  —  l-h'  nil  .  .  .  M„"m„^  0.      (68) 

(In  applying  this  formula  to  various  bodies,  it  is  to  be  observed  that 
only  the  values  of  the  unaccented  letters  are'  to  be  determined  by 
the  different  bodies  to  which  it  is  applied,  the  values  of  the  accented 
letters  being  already  determined  by  the  given  fluid.)  Now,  by  (60), 
(65),  and  (67),  the  value  of  the  first  member  of  this  condition  is  zero 
when  applied  to  the  solid  in  its  given  state.  As  the  condition  must 
hold  true  of  a  body  differing  infinitesimally  from  the  solid,  we  shall 
have 

dt'  —  t"  dif  -\-p"  di^'  —  l^i„"  dnij  .   .  .   ^"  dnij 

—  f.i,,"  dm,!  ...  -  /V'fW=  0,      (69) 

or,  by  equations  (58)  and  (65), 

{l-i,,' —  l^a')  dm,;  .  .  .  -[_(//,/-;/;')  c?;/,; 

+  {Ih'-^u")  dm,;  ...   4-  (/V-yWi")  dm,'^  0.  (70) 

Therefore,  as  these  differentials  are  all  independent, 

^,;  =  Ma",  ■  ■  •  mJ  =  mJ\  M>'=  /■</'',  '  •  •  Mh'^  /'x";  (71) 
which  with  (65)  are  evidently  the  same  conditions  which  we  would 
have  obtained  if  we  had  neglected  the  fact  of  the  solidity  of  one  of 
the  masses. 


J.    W.  Gibhs — Equilibrium  of  Heteroyentous  /Substances.       1)37 

We  have  supposed  the  solid  to  be  homogeneous.  But  it  is  evident 
that  in  any  case  the  above  conditions  must  hold  for  every  separate 
point  where  the  solid  meets  the  fluid.  Hence,  the  temperature  and 
pressure  and  the  potentials  for  all  the  actual  components  of  the  solid 
must  have  a  constant  value  in  the  solid  at  the  surface  where  it  meets 
the  fluid.  Now,  these  quantities  are  determined  by  the  nature  and 
state  of  the  solid,  and  exceed  in  number  the  independent  variations 
of  which  its  nature  and  state  ai'e  capable.  Hence,  if  we  reject  as 
improbable  the  supposition  that  the  nature  or  state  of  a  body  can 
vary  Avithout  affecting  the  value  of  any  of  these  quantities,  we  may 
conclude  that  a  solid  which  varies  (continuously)  in  nature  or  state 
at  its  surface  cannot  be  in  equilibrium  with  a  stable  fluid  which  con- 
tains, as  independently  variable  components,  the  variable  components 
of  the  solid.  (There  may  be,  however,  in  equilibrium  with  the  same 
stable  fluid,  a  finite  number  of  different  solid  bodies,  composed  of  the 
variable  components  of  the  fluid,  and  having  their  nature  and  state 
completely  determined  by  the  fluid.)* 

Effect  of  Additional  Equations  of  Condition. 

As  the  equations  of  condition,  of  which  we  have  made  use,  are 
such  as  always  apply  to  matter  enclosed  in  a  rigid,  impermeable,  and 
non-conducting  envelop,  the  particular  conditions  of  equilibrium 
which  we  have  found  will  always  be  sufficient  tor  equilibrium.  But 
the  number  of  conditions  necessary  for  equilibrium,  will  be  dimin- 
ished, in  a  case  otherwise  the  same,  as  the  number  of  equations 
of  condition  is  increased.  Yet  the  problem  of  equilibrium  which  has 
been  treated  will  sufficiently  indicate  the  method  to  be  pursued  in  all 
cases  and  the  general  nature  of  the  results. 

It  will  be  observed  that  the  position  of  the  various  homogeneous 
parts  of  the  given  mass,  which  is  otherwise  immaterial,  may  deter- 
mine the  existence  of  certain  equations  of  condition.  Thus,  when 
difterent  parts  of  the  system  in  which  a  certain  substance  is  a  vari- 
able component  are  entirely  separated  from  one  another  by  parts  of 
which  this  substance  is  not  a  component,  the  quantity  of  this  sub- 
stance will  be  invariable  for  each  of  the  parts  of  the  system  which  are 
thus  separated,  which  will  be  easily  expressed  by  equations  of  condi- 
tion. Other  equations  of  condition  may  arise  from  the  passive  forces 
.(or  resistances  to  change)  inherent  in  the  given  masses.     In  the  prob- 

*  The  solid  has  been  considered  as  subject  only  to  isotropic  stresses.  The  effect  of 
other  stresses  will  be  considered  hereafter. 

Trans.  Conn.  Acad.,  Vol.  III.  18  November,  1875. 


138      X  W.  Gibbs—Equilihriuin  of  Heterogeneous  Substcmces. 

lem  which  we  are  next  to  consider  there  are  eqnations  of  condition 
due  to  a  cause  of  a  different  nature. 

Eff'ect  of  a  Diaphragm  {EqniUbrmm  of  Osmotic  Forces). 

If  the  given  mass,  enclosed  as  before,  is  divided  into  two  parts, 
each  of  which  is  homogeneous  and  fluid,  by  a  diaphragm  which  is 
capable  of  supporting  an  excess  of  pressure  on  either  side,  and  is  per- 
meable to  some  of  the  components  and  impermeable  to  others,  we 
shall  have  the  equations  of  condition 

6,f-\-6v"=%  (72) 

(W=iO,     6v"=0,  (73) 

and  for  the  components  which  cannot  pass  the  diaphragm 

6mJ=0,     dmj'=0,     Sm,,' =  0,     Sm,,"  z=0,     etc.,  (74) 

and  for  those  which  can 

dm,,'  +  d)j/,"=  0,     Sm/  -f  Stn/'  =  0,    etc.  (75) 

With  these  equations  of  condition,  the  general  condition  of  equilib- 
rium (see  (15))  will  give  the  following  particular  conditions: 

t'  =  t",  (76) 

and  for  the  components  which  can  pass  the  diaphragm,  if  actual  com- 
ponents of  both  masses, 

/'//=/'/',     Mt'=^h",    etc.,  (77) 

but  not  2^'  =  p" ■> 

nor  iA,lz=if.i^\     i.(f;  =  ii,'\     etc. 

Again,  if  the  diaphragm  is  pei'meable  to  the  components  in  certain 
proportions  only,  or  in  proportions  not  entirely  determined  yet  sub- 
ject to  certain  conditions,  these  conditions  may  be  expressed  by 
equations  of  condition,  which  will  be  linear  equations  between  6m^\ 
Sm^'t  etc.,  and  if  these  be  known  the  deduction  of  the  i^articular  con- 
ditions of  equilibrium  will  present  no  difficulties.  We  will  however 
observe  that  if  the  components  aS',,  S2,  etc.  (being  actual  components 
on  each  side)  can  pass  the  diaphragm  simultaneously  in  the  propor- 
tions a  J,  a^,  etc.  (without  other  resistances  than  such  as  vanish  with 
the  velocity  of  the  current),  values  proportional  to  a^,  a^,  etc.  are 
possible  for  dni^\  Sm^',  etc.  in  the  general  condition  of  equilibrium, 
6m ^",  Sm^"^  etc.  having  the  same  values  taken  negatively,  so  that 
we  shall  have  for  one  particular  condition  of  equilibrium 

^1  /'/+  "2  '"2'  +  ^^^-  —  '-^1  "  1"  +  ^h  Ih" -^  etc.  (78) 

There  will  evidently  be  as  many  independent  equations  of  this  form 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.      139 

as  there  are  independent  combinations  of  the  elements  which  can 
pass  the  diaj^hragra. 

These  conditions  of  equilibrium  do  not  of  course  depend  in  any 
way  upon  the  supposition  that  the  volume  of  each  fluid  mass  is  kept 
constant,  if  the  diaphragm  is  in  any  case  supposed  immovable.  In 
fact,  we  may  easily  obtain  the  same  conditions  of  equilibrium,  if  we 
suppose  the  volumes  variable.  In  this  case,  as  the  equilibrium  must 
be  preserved  by  forces  acting  upon  the  external  surfaces  of  the  fluids, 
the  variation  of  the  energy  of  the  sources  of  these  forces  must  appear 
in  the  general  condition  of  equilibrium,  which  will  be 

6t'-\-6e"  -^P'  dv'-ifP"  SV'^O,  (79) 

JP  and  P"  denoting  the  external  forces  per  unit  of  area.  (Compare 
(14).)  From  this  condition  we  may  evidently  derive  the  same 
internal  conditions  of  equilibrium  as  before,  and  in  addition  the 
external  conditions 

p'  —  P\    p"z=P".  (80) 

In  the  preceding  paragraphs  it  is  assumed  that  the  permeability  of 
the  diajjhragm  is  perfect,  and  its  impermeability  absolute,  i.  e.,  that  it 
offers  no  resistance  to  the  passage  of  the  components  of  the  fluids  in 
certain  proportions,  except  such  as  vanishes  with  the  velocity,  and 
that  in  other  proportions  the  components  cannot  pass  at  all.  How 
far  these  conditions  are  satisfied  in  any  particular  case  is  of  course  to 
be  determined  by  experiment. 

If  the  diaphragm  is  permeable  to  all  the  n  components  without 
restriction,  the  temperature  and  the  potentials  for  all  the  components 
must  be  the  same  on  both  sides.  Now,  as  one  may  easily  convince 
himself,  amass  having  n  components  is  capable  of  only /i  +  1  inde- 
pendent variations  in  nature  and  state.  Hence,  if  the  fluid  on  one 
side  of  the  diaphragm  remains  without  change,  that  on  the  other  side 
cannot  (in  general)  vary  in  nature  or  state.  Yet  the  pressure  will 
not  necessarily  be  the  same  on  both  sides.  For,  although  the  pres- 
sure is  a  function  of  the  temperature  and  the  n  potentials,  it  may  be 
a  many-valued  function  (or  any  one  of  several  functions)  of  these 
variables.  But  when  the  pi-essures  are  different  on  the  two  sides, 
the  fluid  which  has  the  less  pressure  will  be  practically  unstable,  in 
the  sense  in  which  the  term  has  been  used  on  page  133.     For 

£"_?;"  7/' +/>"?/'—/.</'»*,"  — /1 2" ??^2"  .  .  .  — //„"/>/„"  =  0,  (SI) 
as  appears  from  equation  (12)  if  integrated  on  the  supposition  that 
the  nature  and  state  of  the  mass  remain  unchanged.  Therefore,  if 
p<}j"  while  t'-t'\  ;t,'=  ;:,",  etc. 


140      J.  W.  Gibbs — Equilibrmm  of  Heteroge)ieous  ^Substances. 

f,"  _t' //' -\-p'v"- /.i^'m,"  -  J^to'ms"  .  .  .    - /-'n  m„" <^0.      (82) 

This  relation  indicates  the  instability  of  tlie  fluid  to  which  the  single 
accents  refer.     (See  page  133.) 

But  independently  of  any  assumption  in  regard  to  the  permeability 
of  the  diaphragm,  the  following  relation  will  hold  true  in  any  case  in 
which  eacli  of  the  two  fluid  masses  may  be  regarded  as  unifonn 
throughout  in  nature  and  state.  Let  the  character  d  be  used  with 
the  variables  which  express  the  nature,  state,  and  quantity  of  the 
fluids  to  denote  the  increments  of  the  values  of  these  quantities  actu- 
ally occurring  in  a  time  either  flnite  or  infinitesimal.  Then,  as  the 
heat  received  by  the  two  masses  cannot  exceed  t'T>}/  -\-t"  v>if',  and  as 
the  increase  of  their  energy  is  equal  to  the  difference  of  the  heat 
they  receive  and  the  work  they  do, 

Di'  +  T>b"  -St' litf  +  «"d//'  — />'du'—  p"iyv",  (83) 

i.e.,  by  (12), 

yu,'Dm,'+/(i"Dm/'  +  //2'n?;4'  +  /<2"Dm2"  +  etc.  ^0,      (84) 

or 

(///'  —  ///)  r.m/'+  (/^2"-/^2')  ^>m,"+  etc.  ^0.  (85) 

It  is  evident  that  the  sign  =  liolds  true  only  in  the  limiting  case  in 
which  no  motion  takes  place. 

DEFINITION    AND    PROPERTIES    OF    FUNDAMENTAL    EQUATIONS. 

The  solution  of  the  problems  of  equilibrium  which  we  have  been 
considering  has  been  made  to  depend  upon  the  equations  which 
express  the  relations  between  the  energy,  entropy,  volume,  and  the 
quantities  of  the  various  components,  for  homogeneous  combinations 
of  the  substances  which  are  found  in  the  given  mass.  The  nature  of 
such  equations  must  be  determined  by  experiment.  As,  however,  it 
is  only  differences  of  energy  and  of  entropy  that  can  be  measured,  or 
indeed,  that  have  a  physical  meaning,  the  values  of  these  quantities 
are  so  far  arbitrary,  that  we  may  choose  independently  for  each 
simple  substance  the  state  in  which  its  energy  and  its  entropy  are 
both  zero.  The  values  of  the  energy  and  .the  entropy  of  any  com- 
pound body  in  any  particular  state  will  then  be  fixed.  Its  energy 
will  be  the  sum  of  the  work  and  heat  expended  in  bringing  its  com- 
ponents from  the  states  in  which  their  energies  and  their  entropies 
are  zero  into  combination   and   to  the  state  in   question  ;    and  its 

entropy  is  the  value  of  the  integral   /  —  for  any  reversible  process 


J.  W.  Gibbs — Equilibrium  of  Hetei'ogeiieoiis  Substances.      141 

by  which  that  change  is  effected  [dQ  denoting  an  element  of  the 
heat  communicated  to  the  matter  thns  treated,  and  t  the  temperature 
of  the  matter  receiving  it).  In  the  determination  botli  of  the  energy 
and  of  the  entropy,  it  is  understood  that  at  the  close  of  the  process, 
all  bodies  whicli  have  been  used,  other  than  those  to  which  the  deter- 
minations relate,  have  been  restored  to  their  original  state,  with  the 
exception  of  the  sources  of  the  work  and  heat  expended,  which  must 
be  used  only  as  such  sources. 

We  know,  however,  a  priori,  that  if  the  quantity  of  any  homoge- 
neous mass  containing  it.  independently  variable  components  varies 
and  not  its  nature  or  state,  the  quantities  f,  ?/,  v,  »i,,  m^,  .  .  .  ni„  will 
all  vary  in  the  same  proportion  ;  therefore  it  is  sufficient  if  we  learn 
from  experiment  the  relation  between  all  but  any  one  of  these  quan- 
tities for  a  given  constant  value  of  that  one.  Or,  we  may  consider 
that  we  have  to  learn  from  experiment  the  relation  subsisting 
between  the  n  i-  2  ratios  of  the  n -{- 3  quantities  f,  //,  v,  m^,  ra^, 

.  .  .  m„.     To  fix  our  ideas  we  may  take  for  these  ratios    ,  -,  — ?,  — -. 

etc.,  that  is,  the  separate  densities  of  the  components,  and  the  ratios 

£  If 

-  and  -,  which  may  be  called  the  densities  of  energy  and  entropy. 
But  when  there  is  but  one  comj^onent,  it  may  be  more  convenient  to 

choose  — ,  — ,  —  as  the  three  variables.     In  any  case,  it  is  only  a  func- 

m    ni,   ni  j  7  ., 

tion  of  w.  -f-  1  independent  variables,  of  which  the  form  is  to  be  deter- 
mined by  experiment. 

Now  if  £  is  a  known  function  of  ;/,  w,  m^,  m^,  .  .  .  m^,  as  by  equa- 
tion (12) 

de-=.td)]  -  p  dv  +  // ,  dm  j  -|-  /ig  ^^2   •   •   •    +  /v„  dm„,         (86) 

t,p,'  1^1,  ^2')  •  •  •  A'n  ^'"^  functions  of  the  same  variables,  which  may 
be  derived  from  the  original  function  by  differentiation,  and  may 
therefore  be  considered  as  known  functions.  This  will  make  n  -\-  S 
independent  known  relations  between  the  2n  +  5  variables,  e,  /;,  v 
m^,  7712,  •  •  •  "^n»  t,P,  /-^i-,  1^2,  ■  ■  ■  /'n-  These  are  all  that  exist,  for 
of  these  variables,  n  +  2  are  evidently  independent.  Now  upon 
these  relations  depend  a  very  large  class  of  the  properties  of  the 
compound  considered,  —we  may  say  in  general,  all  its  thermal, 
mechanical,  and  chemical  properties,  so  far  as  active  tendencies  are 
concerned,  in  cases  in  which  the  form  of  the  mass  does  not  require 
consideration.     A  single  equation  from  which  all  these  relations  may 


142      J.  W.  Gihbs  —Equilibrluiii.  of  Heterogeneous  Substances. 

be  deduced  we  will  call  a  fundamental  equation  for  the  substance  in 
question.  We  shall  hereafter  consider  a  more  general  form  of  the  fun- 
damental equation  for  solids,  in  which  the  pressure  at  any  point  is  not 
supposed  to  be  the  same  in  all  directions.  But  for  masses  subject  only 
to  isotropic  stresses  an  equation  between  f,  //,  w,  m^,m^,  .  .  .  m„  is 
a  fundamental  equation.  There  are  other  equations  which  possess 
this  same  property.* 
Let 

'/'=f-^'A  (87) 

then  by  differentiation  and  comparison  with  (86)  we  obtain 

d  ij'  =z  —  i/dt  —  pdv  -f-  /^j  dni^  -\-  m^  dm^   .  .  .    +  /.i^dm^.     (88) 

If,  then,  y-  is  known  as  a  function  of  t,  v,  m^,  m.^,  .  .  .  m„,  we  can 
find  If,  p,  J-i  1,  /'■>,  •  ■  •  A'n  i"  terms  of  the  same  variables.  If  we  then 
substitute  for  //'  in  our  original  equation  its  value  taken  from  eq.  (87), 
we  shall  have  again  7i  -\-  3  independent  relations  between  the  same 
2n  +  5  variables  as  before. 

Let 

X=£+pv,  (89) 

then  by  (86), 

dx  —  tdi]  +  V  dp  4-/^1  dm^  +  //g  dm^   ...    -|-  //„  drn^.       (90) 

If,  then,  X  be  known  as  a  function  of  }i,p,  m^,  m.^,  .  ,  .  rn„,  we  can 
find  t,  V,  yUj,  /<2»  •  •  •  /^n  i"  terms  of  the  same  variables.  By  elimi- 
nating J,  we  may  obtain  again  n  +  3  independent  relations  between 
the  same  2?/  +  5  variables  as  at  first. 

Let 

^  =  e  -  ttf  +pv,  (91) 

then,  by  (86) 

di^=:.  —  ffdt  +  V  dp  +  ;<j  dm^  +  1.(2  dm „   .  .  .    +  ^^dm^.      (92) 

If,  then,  ^  is  known  as  a  function  of  ^,  /?,  mj,  mg,  .  .   .  ;;?„,  we  can 

*  M.  Massieu  (Comptes  Rendus,  T.  Ixix,  1869,  p.  858  and  p.  1057)  has  shown 
how  all  the  properties  of  a  fluid  "  which  are  considered  in  thermodynamics"  may  be 
deduced  from  a  single  function,  which  he  calls  a  characteristic  function  of  the  fluid 
considered.  In  the  papers  cited,  he  introduces  two  different  functions  of  this  kind ; 
viz.,  a  function  of  the  temperature  and  volume,  which  he  denotes  by  1/),  the  value  of 

—  t  +  tn      ~  f 

which  in  our  notation  would  be 7 or  — r—  ;  and  a  function  of  the  temperature 

and  pressure,  which  he  denotes  by  V^',  the  value  of  which  in   our  notation  would  be 

—  e  +  tr/  —pv       —  C 

1 or  -7-.     In  both  cases  he  considers  a  constant  quantity  (one  kilogram) 

of  the  fluid,  which  is  regarded  as  invariable  in  composition. 


J.  W.  Gibbs — JEquilibrlum  of  Heterogeneous  Substances.      143 

find  If,  V,  yUj,  /.i.j,,  •  •  •  Mn  i^i  terms  of  the  same  variables.  By  elimi- 
nating C,  we  may  obtain  again  n  -{-  S  independent  relations  between 
the  same  2n  +  5  variables  as  at  first. 

If  we  integrate  (86),  supposing  the  quantity  of  the  compound  sub- 
stance considered  to  vary  from  zero  to  any  finite  value,  its  nature 
and  state  remaining  unchanged,  we  obtain 

s=ztff  —  pv  +  /^  1  in  J  +  //^  »« 3   .  .  .    +  //„  ?n„,  (93 ) 

and  by  (87),  (89),  (91) 

Tlie  last  three  equations  may  also  be  obtained  directly  by  integrating 
(88),  (90),  and  (92). 

If  we  differentiate  (93)  in  the  most  general  manner,  and  compare 
the  result  with  (86),  we  obtain 

—  V  dp  -\-  tjdt  +  m^  dfi^  -\-  in^  dji^   .  .  .    +  )n„dii„-=.  0,       (97) 
or 

dp=i-  dt  H i  <?/<!  H df.i^  .  .  .    H df.1^  =  0.        (98) 

Hence,  there  is  a  relation  between  the  n  +  2  quantities  t,  p,  jli^,  fi.^, 
.  .  .  yt/„,  which,  if  known,  will  enable  us.  to  find  in  terms  of  these  quan- 
tities all  the  ratios  of  the  n  +  2  quantities  //,  v,  m^,  m^  .  .  .  m„. 
With  (93),  this  will  make  n  +  S  independent  relations  between  the 
same  2n  +  5  variables  as  at  first. 

Any  equation,  therefore,  between  the  quantities 


+  /v„  m„. 

(94) 

+  Mn  w„, 

(95) 

+  //„m„. 

(96) 

f, 

V, 

V, 

m„ 

■/7<3,    .    . 

.   rn„, 

(99) 

or 

'/', 

f, 

V, 

mj. 

m^,  .  . 

•  m„, 

(100) 

or 

A', 

V, 

Ih 

rn^, 

^2,  .  , 

.  .   m„, 

(101) 

or 

^, 

t, 

P. 

mi, 

"*2,    • 

■  '  m„, 

(102) 

or 

t, 

P, 

/<i, 

l-lo,     . 

.     ■      l-ln, 

(103) 

is  a  fundamental  equation,  and  any  such  is  entirely  equivalent  to  any 
other.*  For  any  homogeneous  mass  whatever,  considered  (in  gen- 
eral) as  variable  in  composition,  in  quantity,  and  in  thermodynamic 
state,  and  having  n  independently  variable  components,  to   which 

*  The  distinction  between  equations  which  are,  and  which  are  not,  fundamental,  in 
the  sense  in  whicli  the  word  is  here  used,  may  be  illustrated  by  comparing  an  equation 


144      J.  W.  Glhbs  —Equilibriuin  of  Heterogeneous  Substances. 

the  subscript  nuraertils  refer,  (but  not  excluding  tlie  case  in  which 
//  z=  1  and  the  composition  of  tlie  body  is  invariable,)  there  is  a  rela- 
tion between  the  quantities  enumerated  in  any  one  of  the  above  sets, 
from  which,  if  known,  with  the  aid  only  of  general  principles  and 
relations,  we  may  deduce  all  the  relations  subsisting  for  such  a  mass 
between  the  quantities  e,  i/-,  x,  I',  '/,  v,  rjt  ^,  m.^,  .  .  ,  ///„,  t, p,  /.ij,  ju.^, 
.  .  .  //„.  It  will  be  observed  that,  besides  the  equations  which 
define  i/:,  x,  and  'C,  there  is  one  finite  equation,  (93),  which  subsists 
between  these  qiiantities  independently  of  the  form  of  the  fundamental 
equation. 

Other  sets  of  quantities  might  of  course  be  added  which  possess 
the  same  property.  The  sets  (100),  (101),  (102)  are  mentioned  on 
account  of  the  important  properties  of  the  quantities  i/-,  j,  'Q,  and 
because  the  equations  (88),  (90),  (92),  like  (86),  ufiTord  convenient 
definitions  of  the  potentials,  viz., 

;,,=(*)  ={'PL)  =(m  =(^)  (104) 

etc.,  where  the  subscript  letters  denote  the  quantities  which  remain 
constant  in  the  differentiation,  m  being  written  for  brevity  for  all  the 
letters  m^,  mg,  .  .  .  in„  except  the  one  occurring  in  the  denominator. 
It  will  be  observed  that  the  quantities  in  (103)  are  all  independent 
of  the  quantity  of  the  mass  considered,  and  are  those  which  must,  in 
general,  have  the  same  value  in  contiguous  masses  in  equilibrium. 

0)1  the  quantities  i/\  j,  t. 
The  quantity  //'  has  been  defined  for  any  homogeneous  mass  by  the 

equation 

if'  -€  ~  tt].  (105) 

between 


e,  J],  V,  m,,  m,,  . 

.    .    Win 

with  one  between 

c,  t,v,  m,,  mo,  . 

■  .  in„. 

As,  by  (86), 

de 

) 

the  second  equation  may  evidently  be  derived  from  the  first.     But  the  first  equation 
cannot  be  derived  from  the  second;  for  an  equation  between 

^'    \dn)     -   ^.   "in  w?)    •    •    •    w„ 


Kd?! 

is  equivalent  to  one  between 

drj 
de 


f,  V,  m,,  m.^,  .  .  .  m„. 


which  is  evidently  not  sufficient  to  determine  the  value  of  ?/  in  terms  of  the  other 
variables. 


J.  W.  Gihbs — Equilibrium  of  Heterogeneous  Substances.      145 

We  may  extend  this  definition  to  any  material  system  whatever 
which  has  a  nniform  temperature  throughout. 

If  we  compare  two  states  of  the  system  of  the  same  temperature, 
we  have 

f-f'  =  f'- 6" -?;(;/  -,/').  (106) 

If  we  suppose  the  system  brought  from  the  first  to  the  second  of 
these  states  without  change  of  temperature  and  by  a  reversible  pro- 
cess in  which  W  is  the  work  done  and  Q  the  heat  received  by  the 
system,  then 

£'-f":rrTF-  Q,  (107) 

and  t{if'  ^  i/)=Q.  (108) 

Hence 

//''-//'"  =  IF;  (109) 

and  for  an  infinitely  small  reversible  change  in  the  state  of  the 
system,  in  which  the  temperature  remains  constant,  we  may  write 

~dip  =  dW.  (110) 

Therefore,  —  //'  is  the  force  function  of  the  system  for  constant 
temperature,  just  as  —  £  is  the  force  function  for  constant  entropy. 
That  is,  if  we  consider  if:  as  a  function  of  the  temperatm-e  and  the 
variables  which  express  the  distribution  of  the  matter  in  space,  for 
every  different  value  of  the  temperature  —  ?/'  is  the  different  force 
function  required  by  the  system  if  maintained  at  that  special 
temperature. 

From  this  we  may  conclude  that  when  a  system  has  a  uniform 
temperature  throughout,  the  additional  conditions  which  are  necessary 
and  sufficient  for  eqiiilibrium  may  be  expressed  by 

(d^')<^0-*  (111) 

*  This  general  condition  of  equilibrium  might  be  used  instead  of  (2)  in  such  prob- 
lems of  equilibrium  as  we  have  considered  and  others  which  we  shall  consider  here- 
after with  evident  advantage  in  respect  to  the  brevity  of  the  formulas,  as  the  limitation 
expressed  by  the  subscript  i  in  (111)  applies  to  every  part  of  the  system  taken  sepa- 
rately, and  diminishes  by  one  the  number  of  independent  variations  in  the  state  of 
these  parts  which  we  have  to  consider.  The  more  cumbersome  course  adopted  in  this 
paper  has  been  chosen,  among  other  reasons,  for  the  sake  of  deducing  all  the  particular 
conditions  of  equilibrium  from  one  general  condition,  and  of  having  the  quantities 
mentioned  in  this  general  condition  such  as  are  most  generally  used  and  most  simply 
defined ;  and  because  in  the  longer  formulae  as  given,  the  reader  will  easily  see  in  each 
case  the  form  which  they  would  take  if  we  should  adopt  (111)  as  the  general  condi- 
tion of  equilibrium,  which  would  be  in  effect  to  take  the  thermal  condition  of  equilibrium 
for  granted,  and  to  seek  only  the  remaining  conditions.  For  example,  in  the  problem 
treated  on  pages  116  fE.,  we  would  obtain  from  (111)  by  (88)  a  condition  precisely  like 
(15),  except  that  the  terms  16?]',  tSrj"^  etc.  would  be  wanting. 

Trans.  Conn.  Acad.,  Vol.  III.  19  January,  1876. 


146      ./.   W.  Glbbs — Equilibriion  of  IIete)'0(jeneous  SubsUinces. 

When  it  is  not  possible  to  bring  the  system  from  one  to  the  other 
of  the  states  to  which  //''  and  '/'"  relate  by  a  reversible  process  without 
altering  the  temperature,  it  will  be  observed  that  it  is  not  necessary 
for  the  validity  of  (107)-(109)  that  the  temperature  of  the  system 
should  remain  constant  during  the  reversible  process  to  which  TTand 
Q  relate,  provided  that  the  only  source  of  heat  or  cold  used  has  the 
same  temperature  as  the  system  in  its  initial  or  final  state.  Any 
external  bodies  may  be  used  in  the  process  in  any  Avay  not  affect- 
ing the  condition  of  reversibility,  if  restored  to  their  original  con- 
dition at  the  close  of  the  process  ;  nor  does  the  limitation  in  regard 
to  the  use  of  heat  apply  to  such  heat  as  may  be  restored  to  the 
source  from  which  it  has  been  taken. 

It  may  be  interesting  to  show  directly  the  equivalence  of  the  condi- 
tions (111)  and  (2)  when  applied  to  a  system  of  which  the  temperature 
in  the  given  state  is  uniform  throughout. 

If  there  are  any  variations  in  the  state  of  such  a  system  which  do 
not  satisfy  (2),  then  for  these  variations 

6e<Q     and     6}]  =  Q. 

If  the  temperature  of  the  system  in  its  varied  state  is  not  uniform, 
we  may  evidently  increase  its  entropy  without  altering  its  energy 
by  supposing  heat  to  pass  from  the  warmer  to  the  cooler  parts. 
And  the  state  having  the  greatest  entropy  for  the  energy  f  -|-  (Je  will 
necessarily  be  a  state  of  uniform  temperature.  For  this  state  (regarded 
as  a  variation  from  the  original  state) 

dE<Q     and     6i]>Q. 

Hence,  as  we  may  diminish  both  the  energy  and  the  entropy  by  cool- 
ino-  the  system,  there  must  be  a  state  of  uniform  temperature  for 
which  (regarded  as  a  variation  of  the  original  state) 

rff  <  0     and     (J//  =  0. 

From  this  we  may  conclude  that  for  systems  of  initially  uniform  tem- 
perature condition  (2)  will  not  be  altered  if  we  limit  the  variations 
to  such  as  do  not  disturb  the  uniformity  of  temperature. 

Confining  our  attention,  then,  to  states  of  uniform  temperature,  we 
have  by  differentiation  of  (105) 

6s  -  tdi}=dil^-\-})dt.  (112) 

Now  there  are  evidently  changes  in  the  system  (produced  by  heating 
or  cooling)  for  which 

de  -  t  (h/  =  0     and  therefore     Si/^  -[-7jdt=:0,  (113) 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.       147 

neither  S/;  nor  dt  having  the  value  zero.  This  consideration  is  suffi- 
cient to  show  that  the  condition  (2)  is  equivalent  to 

de  —  tdf/^0.  (114) 

and  that  the  condition  (111)  is  equivalent  to 

Sif^-^}/6t^0  .  (115) 

and  by  (112)  the  two  last  conditions  are  equivalent. 

In  such  cases  as  we  have  considered  on  pages  115-137,  in  which 
the  form  and  position  of  the  masses  of  which  the  system  is  composed 
is  immaterial,  uniformity  of  temperature  and  pressure  are  always 
necessary  for  equilibrium,  and  the  remaining  conditions,  when  these 
are  satisfied,  may  be  conveniently  expressed  by  means  of  the  func- 
tion ?,  which  has  been  defined  for  a  homogeneous  mass  on  page  142, 
and  which  we  will  here  define  for  any  mass  of  uniform  temperature 
and  pressure  by  the  same  equation 

t,^£  —  ttj-\-pv.  (Ii6) 

For  such  a  mass,  the  condition  of  (internal)  equilibrium  is 

m,,^o.  (117) 

That  this  condition  is  equivalent  to  (2)  will  easily  appear  from  con- 
siderations like  those  used  in  respect  to  (111). 

Hence,  it  is  necessary  for  the  equilibrium  of  two  contiguous  masses 
identical  in  composition  that  the  values  of  C  as  determined  for  equal 
quantities  of  the  two  masses  should  be  equal.  Or,  when  one  of  three 
contiguous  masses  can  be  formed  out  of  the  other  two,  it  is  necessary 
for  equilibrium  that  the  value  of  C  for  any  quantity  of  the  first  mass 
should  be  equal  to  the  sum  of  the  values  of  t.  for  such  quantities  of  the 
second  and  third  masses  as  together  contain  the  same  matter.  Thus, 
for  the  equilibrium  of  a  solution  composed  of  a  parts  of  water  and  b 
parts  of  a  salt  which  is  in  contact  with  vapor  of  water  and  crystals  of 
the  salt,  it  is  necessary  that  the  value  of  t,  for  the  quantity  a-\-b  oi  the 
solution  should  be  equal  to  the  sum  of  the  values  of  C  for  the  quanti- 
ties a  of  the  vapor  and  b  of  the  salt.  Similar  propositions  will  hold 
true  in  more  complicated  cases.  The  reader  will  easily  deduce  these 
conditions  from  the  particular  conditions  of  equilibrium  given  on 
page  128. 

In  like  manner  we  may  extend  the  definition  of  x  to  any  mass  or 

combination  of  masses  in  which  the  pressure  is  everywhere  the  same, 

using  e  for  the  energy  and  v  for  the  volume  of  the  whole  and  setting 

as  before 

X=e-\-pv.  (118) 


148      J.  W.  Gibbs — Eqidlibrium  of  Heterogeneous  Substances. 

If  we  denote  by  Q  the  heat  received  by  the  combined  masses  from 
external  sources  in  any  process  in  which  the  pressure  is  not  varied, 
and  distinguish  the  initial  and  final  states  of  the  system  by  accents 

we  have 

/'  -  /  =  6"  -  6'  +p  {v"  -  v')  =  Q.  (119) 

This  function  may  therefore  be  called  the  heat  function  for  constant 
pressure  (just  as  the  energy  might  be  called  the  heat  function  for 
constant  volume),  the  diminution  of  the  function  representing  in  all 
cases  in  which  the  pressure  is  not  varied  the  heat  given  out  by  the 
system.  In  all  cases  of  chemical  action  in  which  no  heat  is  allowed 
to  escape  the  value  of  j  remains  unchanged. 

POTENTIALS. 

In  the  definition  of  the  potentials  /i^,  /Yg,  etc.,  the  energy  of  a 
homogeneous  mass  was  considered  as  a  function  of  its  entropy,  its 
volume,  and  the  quantities  of  the  various  substances  composing  it. 
Then  the  potential  for  one  of  these  substances  was  defined  as  the  dif- 
ferential coefficient  of  the  energy  taken  with  respect  to  the  variable 
expressing  the  quantity  of  that  substance.  Now,  as  the  manner  in 
which  we  consider  the  given  mass  as  composed  of  various  substances 
is  in  some  degree  arbitrary,  so  that  the  energy  may  be  considered  as 
a  function  of  various  different  sets  of  variables  expressing  quantities 
of  component  substances,  it  might  seem  that  the  above  definition 
does  not  fix  the  value  of  the  potential  of  any  substance  in  the  given 
mass,  until  we  have  fixed  the  manner  in  which  the  mass  is  to  be  con- 
sidered as  composed.  For  example,  if  we  have  a  solution  obtained 
by  dissolving  in  water  a  certain  salt  containing  water  of  crystalliza- 
tion, we  may  consider  the  liqviid  as  composed  of  nig  weight-units  of  the 
hydrate  and  myy  of  water,  or  as  composed  of  m,  of  the  anhydrous 
salt  and  w„,  of  water.  It  will  be  observed  that  the  vahies  of  m,,  and 
m,  are  not  the  same,  nor  those  of  m„-  and  m,,,,  and  hence  it  might 
seem  that  the  potential  for  water  in  the  given  liquid  considered  as 
composed  of  the  hydrate  and  water,  viz., 

(^\ 

\d»ijy/fi,  V,  ms 

would  be  different  from  the  potential  for  water  in  the  same  liquid  con- 
sidered as  composed  of  anhydrous  salt  and  water,  viz., 


J.  W.  Gihbs — EquiUhrlum  of  Heterogeneous  ISuhstances.       149 

The  value  of  the  two  expressions  is,  however,  the  same,  for,  although 
?>?„•  is  not  equal  to  w„,,  we  may  of  course  suppose  chuyy  to  he  equal  to 
clm^,  and  then  the  numerators  in  the  two  fractions  will  also  be  equal, 
as  they  each  denote  the  increase  of  energy  of  the  liquid,  when  the 
quantity  (hn^y  or  drn^,  of  water  is  added  without  altering  the  entropy 
and  volume  of  the  liquid.  Precisely  the  same  considerations  will 
apply  to  any  other  case. 

In  fact,  we  may  give  a  definition  of  a  potential  which  shall  not  pre- 
suppose any  choice  of  a  particular  set  of  substances  as  the  components 
of  the  homogeneous  mass  considered. 

Definition. — If  to  any  homogeneous  mass  we  suppose  an  infinitesi- 
mal quantity  of  any  substance  to  be  added,  the  mass  remaining 
homogeneous  and  its  entropy  and  volume  remaining  unchanged,  the 
increase  of  the  energy  of  the  mass  divided  by  the  quantity  of  the 
substance  added  is  the  potential  for  that  substance  in  the  mass  con- 
sidered. (For  the  purposes  of  this  definition,  any  chemical  element  or 
combination  of  elements  in  given  proportions  may  be  considered  a 
substance,  whether  capable  or  not  of  existing  by  itself  as  a  homoge- 
neous body.) 

In  the  above  definition  we  may  evidently  substitute  for  entropy, 
volume,  and  energy,  respectively,  either  temperature,  volume,  and 
the  function  ij- ;  or  entropy,  pressure,  and  the  function  x ;  or  tempera- 
ture, pressure,  and  the  function  ;;.     (Compare  equation  (104).) 

In  the  same  homogeneous  mass,  therefore,  we  may  distinguish  the 
potentials  for  an  indefinite  number  of  substances,  each  of  which  has  a 
perfectly  determined  value. 

Between  the  potentials  for  diiferent  substances  in  the  same  homo- 
geneous mass  the  same  equations  will  subsist  as  between  the  units 
of  these  siibstances.  That  is,  if  the  substances,  *S„,  /S',„  etc.,  ^S^,  Si,  etc., 
are  components  of  any  given  homogeneous  mass,  and  are  such  that 

a  2„  +  /^  g,  +  etc.  =  n  ©,  +  ^  ©/+  etc.,  (120) 

©a,  S45  etc.,  2i,  S/,  etc.  denoting  the  units  of  the  several  substances, 
and  «,  /j,  etc.,  «,  A,  etc.  denoting  numbers,  then  if  /<„,  ^,„  etc.,  /z^,  /^„ 
etc.  denote  the  potentials  for  these  substances  in  the  homogeneous 

mass, 

a  i-ia  +  /^  yWi  +  etc.  =  H  f-ik  +  A  /^,  +  etc.  (121) 

To  show  this,  we  will  suppose  the  mass  considered  to  be  very  large. 
Then,  the  first  number  of  (121)  denotes  the  increase  of  the  energy  of 
the  mass  produced  by  the  addition  of  the  matter  represented  by  the 
first  member  of  (120),  and  the  second  member  of  (121)  denotes  the 


150      J.  W.  Gibbs — Equilibrmrn  of  Heterogeneous  Substances. 

increase  of  energy  of  the  same  mass  produced  by  the  addition  of  the 
matter  represented  by  the  second  member  of  (120),  the  entropy  and 
volume  of  the  mass  remaining  in  each  case  unchanged.  Therefore,  as 
the  two  members  of  (120)  represent  the  same  matter  in  kind  and 
quantity,  the  two  members  of  (121)  must  be  equal. 

But  it  must  be  understood  that  equation  (120)  is  intended  to 
denote  equivalence  of  the  substances  represented  in  the  mass  con- 
sidered, and  not  merely  chemical  identity  ;  in  other  words,  it  is  sup- 
posed that  there  are  no  passive  resistances  to  change  in  the  mass 
considered  which  prevent  the  substances  represented  by  one  member 
of  (120)  from  passing  into  those  represented  by  the  other.  For 
example,  in  respect  to  a  mixture  of  vapor  of  water  and  free  hydrogen 
and  oxygen  (at  ordinary  temperatures),  we  may  not  write 

but  water  is  to  be  treated  as  an  independent  substance,  and  no  neces- 
sary relation  will  subsist  between  the  potential  for  water  and  the 
potentials  for  hydrogen  and  oxygen. 

The  reader  will  observe  that  the  relations  expressed  by  equations 
(43)  and  (51)  (which  are  essentially  relations  between  the  poten- 
tials for  actual  components  in  different  parts  of  a  mass  in  a  state  of 
equilibrium)  are  simply  those  which  by  (121)  would  necessary  sub- 
sist between  the  same  potentials  in  any  homogeneous  mass  containing 
as  variable  components  all  the  substances  to  which  the  potentials 
relate. 

In  the  case  of  a  body  of  invariable  composition,  the  potential  for 
the  single  component  is  equal  to  the  value  of  t,  for  one  unit  of  the 
body,  as  appears  from  the  equation 

1;=: /.nn  (122) 

to  which  (96)  reduces  in  this  case.  Therefore,  when  n  =  \,  the  fun- 
damental equation  between  the  quantities  in  the  set  (102)  (see  page 
143)  and  that  between  the  quantities  in  (103)  may  be  derived  either 
from  the  other  by  simple  substitution.  But,  with  this  single  excep- 
tion, an  eqiiation  between  the  quantities  in  one  of  the  sets  (99)-(103) 
cannot  be  derived  from  the  equation  between  the  quantities  in 
another  of  these  sets  without  differentiation. 

Also  in  the  case  of  a  body  of  variable  composition,  when  all  the 
quantities  of  the  components  except  one  vanish,  the  potential  for 
that  one  will  be  equal  to  the  value  of  t,  for  one  unit  of  the  body. 
We  may  make  this  occur  for  any  given  composition  of  the  body  by 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.      15] 

choosing  as  one  of  the  components  the  matter  constituting  the  body 
itself,  so  that  the  value  of  ?  for  one  unit  of  a  body  may  always  be 
considered  as  a  potential.  Hence  the  relations  between  the  values  of 
?  for  contiguous  masses  given  on  page  1 47  may  be  regarded  as  rela- 
tions between  potentials. 

The  two  following  propositions  afford  definitions  of  a  potential 
which  may  sometimes  be  convenient. 

The  potential  for  any  substance  in  any  homogeneous  mass  is  equal 
to  the  amount  of  mechanical  work  required  to  bring  a  unit  of  the 
substance  by  a  reversible  process  from  the  state  in  which  its  energy 
and  entropy  are  both  zei'o  into  combination  with  the  homogeneous 
mass,  which  at  the  close  of  the  process  must  have  its  original  volume, 
and  which  is  supposed  so  large  as  not  to  be  sensibly  altered  in  any 
part.  All  other  bodies  used  in  the  process  must  by  its  close  be 
restored  to  their  oi'iginal  state,  except  those  used  to  supply  the 
work,  which  must  be  used  only  as  the  source  of  the  work.  For,  in 
a  reversible  process,  when  the  entropies  of  other  bodies  are  not 
altered,  the  entropy  of  the  substance  and  mass  taken  together  will 
not  be  altered.  But  the  original  entropy  of  the  substance  is  zero; 
therefore  the  entropy  of  the  mass  is  not  altered  by  the  addition  of  the 
substance.  Again,  the  work  expended  will  be  equal  to  the  increment 
of  the  energy  of  the  mass  and  substance  taken  together,  and  therefore 
equal,  as  the  original  energy  of  the  substance  is  zero,  to  the  increment 
of  energy  of  the  mass  due  to  the  addition  of  the  substance,  which  by 
the  definition  on  page  149  is  equal  to  the  potential  in  question. 

The  potential  for  any  substance  in  any  homogeneous  mass  is  equal 
to  the  work  required  to  bring  a  unit  of  the  substance  by  a  reversible 
process  from  a  state  in  which  //'  =  0  and  the  temperature  is  the  same 
as  that  of  the  given  mass  into  combination  with  this  mass,  which  at 
the  close  of  the  process  must  have  the  same  volume  and  temperature 
as  at  first,  and  which  is  supposed  so  large  as  not  to  be  sensibly 
altered  in  any  part.  A  source  of  heat  or  cold  of  the  temperature 
of  the  given  mass  is  allowed,  with  this  exception,  other  bodies  are 
to  be  used  only  on  the  same  conditions  as  before.  This  may  be 
shown  by  applying  equation  (109)  to  the  mass  and  substance  taken 
together. 

The  last  proposition  enables  us  to  see  very  easily,  how  the  value  of 
the  potential  is  affected  by  the  arbitrary  constants  involved  in  the 
definition  of  the  energy  and  the  entropy  of  each  elementary  sub- 
stance. For  we  may  imagine  the  substance  brought  from  the  state 
in  which  tp=zQ  and  the  temperature  is  the  same  as  that  of  the  given 


152      J.W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 

mass,  first  to  any  specified  state  of  the  same  temperature,  and  then 
into  combination  with  the  given  mass.  In  the  first  part  of  the  pro- 
cess the  work  expended  is  evidently  represented  by  the  value  of  y.' 
for  the  unit  of  the  substance  in  the  state  specified.  Let  this  be 
denoted  by  </'',  and  let  /<  denote  the  potential  in  question,  and  W  the 
work  expended  in  bringing  a  unit  of  the  substance  from  the  specified 
state  into  combination  with  the  given  mass  as  afoi-esaid ;  then 

lx=ip'-^W.  (123) 

Now  as  the  state  of  the  substance  for  which  6=0  and  ?/  =  0  is 
arbitrary,  we  may  simultaneously  inci-ease  the  energies  of  the  unit  of 
the  substance  in  all  possible  states  by  any  constant  C,  and  the 
entropies  of  the  substance  in  all  possible  states  by  any  constant  K. 
The  value  of  //•,  or  £  —  t  //,  for  any  state  would  then  be  increased  by 
C  -^  t  K,  t  denoting  the  temperature  of  the  state.  Applying  this 
to  if:'  in  (123)  and  observing  that  the  last  term  in  this  equation  is 
independent  of  the  values  of  these  constants,  we  see  that  the  potential 
would  be  increased  by  the  same  quantity  C  —  t  K,  t  being  the  tem- 
perature of  the  mass  in  which  the  potential  is  to  be  determined. 

ON    COEXISTENT   PHASES    OF    MATTER. 

In  considering  the  different  homogeneous  bodies  which  can  be 
formed  out  of  any  set  of  component  substances,  it  will  be  convenient 
to  have  a  term  which  shall  refer  solely  to  the  composition  and  ther- 
modynamic state  of  any  such  body  without  regard  to  its  quantity  or 
form.  We  may  call  such  bodies  as  differ  in  composition  or  state  dif- 
ferent phases  of  the  matter  considered,  regarding  all  bodies  which 
differ  only  in  quantity  and  form  as  different  examples  of  the  same 
phase.  Phases  which  can  exist  together,  the  dividing  surfaces  being 
plane,  in  an  equilibrium  which  does  not  depend  upon  passive  resist- 
ances to  change,  we  shall  call  coexistent. 

If  a  homogeneous  body  has  n  independently  variable  components, 
the  phase  of  the  body  is  evidently  capable  of  n.  -|-  1  independent  vari- 
ations. A  system  of  r  coexistent  phases,  each  of  which  has  the  same 
n  independently  variable  components  is  capable  of  «  +  2  —  r  varia- 
tions of  phase.  For  the  temperature,  the  pressure,  and  the  poten- 
tials for  the  actual  components  have  the  same  values  in  the  different 
phases,  and  the  variations  of  these  quantities  are  by  (97)  subject  to 
as  many  conditions  as  there  are  different  phases.  Therefore,  the  num- 
ber of  independent  variations  in  the  values  of  these  quantities,  i.  e., 
the  number  of  independent  variations  of  phase  of  the  system,  will  be 
n+2  -r. 


J,  W.  Gibhs — Equilibrmm  of  Heteroyeneous  Substances.      158 

Or,  when  the  r  bodies  considered  have  not  the  same  independently- 
variable  components,  if  we  still  denote  by  n  the  number  of  indeperud- 
ently  variable  components  of  the  r  bodies  taken  as  a  whole,  the 
number  of  independent  variations  of  phase  of  which  the  system  is 
capable  will  still  be  w+2  —  r.  In  this  case,  it  will  be  necessary  to 
consider  the  potentials  for  more  than  71  component  substances.  Let 
the  number  of  these  potentials  be  n-\-h.  We  shall  have  by  (97),  as 
before,  r  relations  between  the  variations  of  the  temperature,  of  the 
pressure,  and  of  these  n-^h  potentials,  and  we  shall  also  have  by  (43) 
and  (51)  h  relations  between  these  potentials,  of  the  same  form  as  the 
relations  which  subsist  between  the  units  of  the  different  component 
substances. 

Hence,  if  r  =  w  +  2,  no  variation  in  the  phases  (remaining  coex- 
istent) is  possible.  It  does  not  seem  probable  that  r  can  ever  exceed 
n  +  2.  An  example  of  nz=.\  and  rz=.Z  is  seen  in  the  coexistent  solid, 
liquid,  and  gaseous  forms  of  any  substance  of  invariable  composition. 
It  seems  not  improbable  that  in  the  case  of  sulphur  and  some  other 
simple  substances  there  is  more  than  one  triad  of  coexistent  phases ; 
but  it  is  entirely  improbable  that  there  are  four  coexistent  phases  of 
any  simple  substance.  An  example  of  /i  =  2  and  r-=.4:  \s  seen  in  a 
solution  of  a  salt  in  water  in  contact  with  vapor  of  water  and  two 
different  kinds  of  crystals  of  the  salt. 

Concerning  n  -{- \  Coexistent  Phases. 

We  will  now  seek  the  differential  equation  which  expresses  the 
relation  between  the  variations  of  the  tem})erature  and  the  pressure 
in  a  system  of  w  -f  1  coexistent  phases  [n  denoting,  as  before,  the 
number  of  independently  variable  components  in  the  system  taken  as 
a  whole). 

In  this  case  we  have  n  +  1  equations  of  the  general  form  of  (97) 
(one  for  each  of  the  coexistent  phases),  in  which  we  may  distinguish 
the  quantities  //,  v,  m^,  Wg,  etc.  relating  to  the  different  phases  by 
accents.  But  t  and^  will  each  have  the  same  value  throughout,  and 
the  same  is  true  of  /Vj,  /'g,  etc.,  so  far  as  each  of  these  occurs  in  the 
different  equations.  If  the  total  number  of  these  potentials  is  n  +  h, 
there  will  be  h  independent  relations  between  them,  corresponding  to 
the  h  independent  relations  between  the  units  of  the  component  sub- 
stances to  which  the  potentials  relate,  by  means  of  which  we  may 
eliminate  the  variations  of  h  of  the  potentials  from  the  equations  of 
the  form  of  (97)  in  which  they  occur. 

Trans.  Conn.  Acad.,  Vol.  III.  20  January,  1876. 


154      J.  W.  Gihbs — Equilibrium  of  Heterogeneous  Substances. 

Let  one  of  these  equations  be 

v'  dp=z  7]'  dt  +  mj  djj>a  +  "Tin-i  df.ii  +  etc.,  (124) 

and  by  the  proposed  elimination  let  it  become 

v'  dp=  If  dt  +  A^'  dj-i^  +  A^  df.i2  .  .  .  +  A„' d/.j„.  (125) 
It  will  be  observed  that  //„,  for  example,  in  (124)  denotes  the  poten- 
tial in  the  mass  considered  for  a  substance  *S'„  which  may  oi-  may  not 
be  identical  with  any  of  the  substances  S^,  S2,  etc.  to  which  the 
potentials  in  (125)  relate.  Now  as  the  equations  between  the  poten- 
tials by  means  of  which  the  elimination  is  performed  are  similar  to 
those  which  subsist  between  the  units  of  the  corresponding  sub- 
stances, (compare  equations  (38),  (43),  and  (51),)  if  we  denote  these 
units  by  (Sa,  ©4,  etc.,  ©i,  ©g,  etc.,  we  must  also  have 

m„'(S„  +  m;®,,  +  etc.  =  .4j'(5i-|-^2'®2  •  •  •  +^J„'®„-  (126) 
But  the  first  member  of  this  equation  denotes  (in  kind  and  quantity) 
the  matter  in  the  body  to  which  equations  (1 24)  and  (125)  relate.  As 
the  same  must  be  true  of  the  second  memV)er,  we  may  regard  this  same 
body  as  composed  of  the  quantity  A  ^'  of  the  substance  aS,,  with  the 
quantity  A^'  of  the  substance  1S2,  etc.  We  will  therefore,  in  accord- 
ance with  our  general  xisage,  write  m^'  tn^',  etc.  for  A^',  A2',  etc.  in 
(125),  which  will  then  become 

v'  dp  =  7/  dt  -f  »2i'  d/.i^  +  m^  dyi^  •  •  •  +  "*«'  d^^-  (127) 
But  we  must  remember  that  the  components  to  which  the  m/,  mg', 
etc.  of  this  equation  relate  are  not  necessarily  independently  variable, 
as  are  the  components  to  which  the  similar  expressions  in  (9V)  and 
(124)  relate.  The  rest  of  the  /i  +  1  equations  may  be  reduced  to  a 
similar  form,  viz., 

v"  dp  =  7f  dt  -\-  m^"  di-i^  ■^-m^'dj.i^  .  ■  .   +m„"dp„,  (128) 

etc. 
By  elimination  of  f?/<  j,  d/^i^,  .  .  .  dfi„  from  these  equations  we  obtain 


v  m 
v"  m 
v'"     rn 


'"n 

n 

m.^ 

nis 

m: 

v" 

-/' 

?«2 

m„"' 

dp  =. 

v'" 

m/" 

rn^ 

dt.  (129) 


In  this  equation  we  may  make  v',  v",  etc.  equal  to  unity.  Then 
m,',  mg',  m/',  etc.  will  denote  the  separate  densities  of  the  compo- 
nents in  the  different  phases,  and  //',  ?/',  etc.  the  densities  of  entropy. 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.       155 

When  n=L  1, 

{m"  v'  ~  m'  v")  dp  =  {m"  if  -  m  //")  dt,  (130) 

or,  if  we  make  ni'  =.  1  and  m"  =.  1,  we  liave  the  usual  formula 

dt     v'-v"    t{v"-v'y  ^  ^ 

in  which  Q  denotes  the  heat  absorbed  by  a  unit  of  the  substance  in 
passing  from  one  state  to  the  other  without  change  of  temperature  or 
pressure. 

Co7icerning  Cases  in  which  the  Number  of  Coexistent  Phases  is  less 

than  /i-J-  1. 

When  M>  1,  if  the  quantities  of  all  the  components  /S'j,  /Sg,  .  .  .  S„ 
are  proportional  in  two  coexistent  phases,  the  two  equations  of  the 
form  of  (127)  and  (128)  relating  to  these  phases  will  be  sufficient 
for  the  elimination  of  the  variations  of  all  the  potentials.  In  fact, 
the  condition  of  the  coexistence  of  the  two  phases  together  with  the 
condition  of  the  equality  of  the  n —  1  ratios  of  «*/,  m^ ^  ,  .  .  m„' 
with  the  n  —  \  ratios  of  m^\  ^'^-z" ■>  •  •  •  ''*"'  ^^  sufficient  to  detei'mine 
/>  as  a  function  of  t  if  the  fundamental  equation  is  known  for  each  of 
the  phases.  The  ditferential  equation  in  this  case  may  be  expressed 
in  the  form  of  (130),  m'  and  m"  denoting  either  the  quantities  of  any 
one  of  the  components  or  the  total  quantities  of  matter  in  the  bodies 
to  which  they  relate.  Equation  (131)  will  also  hold  true  in  this  case, 
if  the  total  quantity  of  matter  in  each  of  the  bodies  is  unity.  But 
this  case  differs  from  the  preceding  in  that  the  matter  which  absorbs 
the  heat  Q  in  passing  from  one  stat  j  to  another,  and  to  which  the  other 
letters  in  the  formula  relate,  alt-iough  the  same  in  quantity,  is  not  in 
general  the  same  in  kind  at  different  temperatures  and  pressures. 
Yet  the  case  wall  often  occur  that  one  of  the  phases  is  essentially 
invariable  in  composition,  especially  when  it  is  a  crystalline  body, 
and  in  this  case  the  matter  to  which  the  letters  in  (131)  relate  will 
not  vary  with  the  temperature  and  pressure. 

When  n  =  2,  two  coexistent  phases  are  capable,  when  the  temper- 
ature is  constant,  of  a  single  variation  in  phase.  But  as  (130)  will 
hold  true  in  this  case  when  m/  :  m^'  : :  m^"  :  m^",  it  follows  that  for 
constant  temperature  the  pressure  is  in  general  a  maximum  or  a  min- 
imum when  the  composition  of  the  two  phases  is  identical.  In  like 
manner,  the  temperature  of  the  two  coexistent  phases  is  in  general  a 
maximum  or  a  minimum,  for  constant  pi-essure,  when  the  composition 
of  the  two  phases  is  identical.  Hence,  the  series  of  simultaneous 
values  of  t  and  p  for  which  the  composition  of  two  coexistent  phases 


156     J.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 


is  identical  separates  those  simultaneous  values  of  t  and  p  for  which 
no  coexistent  phases  are  possible  from  those  for  which  there  are  two 
pair  of  coexistent  phases.  This  may  be  applied  to  a  liquid  having 
two  independently  variable  compouents  in  connection  with  the  vapor 
which  it  yields,  or  in  connection  with  any  solid  which  may  be  formed 
in  it. 

When   n  =  3,  we  have  for  three  coexistent  phases  three  equations 
of  the  form  of  (127),  from  which  we  may  obtain  the  following, 


V  rn 
v"  m 
v'"  rn 


dp=i 


dt--\- 


m. 


tn. 


djJi^.  (132) 


Now  the  value  of  the  last  of  these  determinants  will  be  zero,  when 
the  composition  of  one  of  the  three  phases  is  such  as  can  be  produced 
by  combining  the  other  two.  Hence,  the  pressure  of  three  coexistent 
phases  will  in  general  be  a  maximum  or  minimum  for  constant  tem- 
perature, and  the  temperature  a  maximum  or  minimvim  for  constant 
pressure,  when  the  above  condition  in  regard  to  the  composition  of 
the  coexistent  phases  is  satisfied.  The  series  of  simultaneous  values 
of  t  and  p  for  which  the  condition  is  satisfied  separates  those  simul- 
taneous values  of  t  and  p  for  which  three  coexistent  phases  are  not 
possible,  from  those  for  which  there  are  two  triads  of  coexistent 
phases.  These  propositions  may  be  extended  to  higher  values  of  ;i, 
and  illustrated  by  the  boiling  temperatures  and  pressures  of  saturated 
solutions  of  ?^  —  2  different  solids  in  solvents  having  two  independ- 
ently variable  components. 

INTERNAL      STABILITY     OF     HOM()(iENEOUS      FLUIDS      AS     INDICATED     BY 
FUNDAMENTAL    EQUATIONS. 

We  will  now  consider  the  stability  of  a  fluid  enclosed  in  a  rigid 
envelop  which  is  non-conducting  to  heat  and  impermeable  to  all  the 
components  of  the  fluid.  The  fluid  is  supposed  initially  homogeneous 
in  the  sense  in  which  we  have  before  used  the  word,  i.  e.,  uniform  in 
every  respect  throughout  its  whole  extent.  Let  <Sj,  S.^.,  ,  .  .  >S„  be 
the  ultiiiiate  components  of  the  fluid  ;  we  may  then  consider  every 
body  which  can  be  formed  out  of  the  fluid  to  be  composed  of  S^,  S2, 
.  .  .  aS„,  and  that  in  only  one  way.  Let  m^,  m^,  .  .  .  m„  denote 
the  quantities  of  these  substances  in  any  such  body,  and  let  f,  ?/,  v, 
denote  its  energy,  entropy,  and  volume.  The  fundamental  equation 
for  compounds  of  iS^,  ^.Sg,  .  .  .  S„,  if  completely  determined,  will  give 
us  all  possible  sets  of  simultaneous  values  of  these  variables  for  homo- 
geneous bodies. 


J.  W.  Gihbs—Equilibriu7n  of  Heterogeneous  Substances.       157 

Now,  if  it  is  possible  to  assign  such  values  to  the  constants  T,  F, 
M^,  J/2,  .  .  .  3f„  that  the  value  of  the  expression 

^  -  T,/-\-Pv  ~  J/,  m,  -  3/2  W2  .  .  .   -  3f„m„  (133) 

shall  be  zero  for  the  given  fluid,  and  shall  be  positive  for  every  other 
phase  of  the  same '  components,  i.  e.,  for  every  homogeneous  body* 
not  identical  in  nature  and  state  with  the  given  fluid  (but  composed 
entirely  oi  S^,  S^,  .  .  .  /S„),  the  condition  of  the  given  fluid  will  be 
stable. 

For,  in  any  condition  whatever  of  the  given  mass,  whether  or  not 
homogeneous,  or  fluid,  if  the  value  of  the  expression  (133)  is  not 
negative  for  any  homogeneous  part  of  the  mass,  its  value  for  the 
whole  mass  cannot  be  negative ;  and  if  its  value  cannot  be  zero  for 
any  homogeneous  part  which  is  not  identical  in  phase  with  the  mass 
in  its  given  condition,  its  value  cannot  be  zero  for  the  whole  except 
when  the  whole  is  in  the  given  condition.  Therefore,  in  the  case 
supposed,  the  value  of  this  expression  for  any  other  than  the  given 
condition  of  the  mass  is  positive.  (That  this  conclusion  cannot  be 
invalidated  by  the  fact  that  it  is  not  entirely  correct  to  regard  a 
composite  mass  as  made  up  of  homogeneous  parts  having  the 
same  properties  in  respect  to  energy,  entropy,  etc.,  as  if  they  were 
parts  of  larger  homogeneous  masses,  will  easily  appear  from  consider- 
ations similar  to  those  adduced  on  pages  131-133.)  If,  then,  the 
value  of  the  expression  (133)  for  the  mass  considered  is  less  when  it 
is  in  the  given  condition  than  when  it  is  in  any  other,  the  energy  of 
the  mass  in  its  given  condition  must  be  less  than  in  any  other  condi- 
tion in  which  it  has  the  same  entropy  and  volume.  The  given  con- 
dition is  therefore  stable.     (See  page  110.) 

Again,  if  it  is  possible  to  assign  such  values  to  the  constants  in 
(133)  that  the  value  of  the  expression  shall  be  zero  for  the  given 
fluid  mass,  and  shall  not  be  negative  for  any  phase  of  the  same  com- 
ponents, the  given  condition  will  be  evidently  not  unstable.  (See 
page  110.)  It  will  be  stable  unless  it  is  possible  for  the  given  matter 
in  the  given  volume  and  with  the  given  entropy  to  consist  of  homo- 
geneous parts  for  all  of  which  the  value  of  the  expression  (133)  is  zero, 
but  which  are  not  all  identical  in  phase  with  the  mass  in  its  given  con- 
dition. (A  mass  consisting  of  such  parts  would  be  in  equilibrium,  as 
we  have  already  seen  on  pages  133,  134.)  In  this  case,  if  we  disre- 
gard  the   quantities  connected  with  the    surfaces  which  divide  the 

*  A  vacuum  is  throughout  this  discussion  to  be  regarded  as  a  limiting  case  of  an 
extremely  rarified  body.  We  may  thus  avoid  the  necessity  of  the  specific  mention  of  a 
vacimm  in  propositions  of  this  kind. 


158      J.  W.  Gihbs — Equilibrium  of  Heterogeneous  Substances. 

homogeneous  parts,  we  must  regard  the  given  condition  as  one  of 
neutral  equilibiium.  But  in  regard  to  these  homogeneous  parts, 
which  we  may  evidently  consider  to  be  all  diiFerent  phases,  the  fol- 
lowing conditions  must  be  satisfied.  (The  accents  distinguish  the 
letters  referring  to  the  different  parts,  and  the  unaccented  letters 
refer  to  the  whole  mass.) 

Tf'  +  jf  +  etc.  =  ;^,  1 

v'  -f  v"  -j-  etc.  =:  y,  I 

m/ +  m/'  +  etc.  =  w,,  1^  (134) 

//?2'  +  ''*3  "  +  etc.  =  ^2,      j 

etc.  J 

Now  the  values  of  //,  y,  m^,  m^,  etc.  are  determined  by  the  whole 

fluid  mass  in  its  given  state,  and  the  values  of  -„  —„  etc.,  —r,  — ^, 
etc —   — -^     etc.,  etc.,  are  determined  by  the  phases  of  the  various 

parts.  But  the  phases  of  these  parts  are  evidently  determined  by 
the  phase  of  the  fluid  as  given.  They  form,  in  fact,  the  whole  set  of 
coexistent  phases  of  which  the  latter  is  one.  Hence,  we  may  regard 
(134)  as  n  +  2  linear  equations  between  ?>',  u",  etc.  (The  values  of 
v'  v"  etc.  are  also  subject  to  the  condition  that  none  of  them  can  be 
negative.)  Now  one  solution  of  these  equations  must  give  us  the 
given  condition  of  the  fluid  ;  and  it  is  not  to  be  expected  that  they 
will  be  capable  of  any  other  solution,  unless  the  number  of  different 
homogeneous  parts,  that  is,  the  number  of  different  coexistent  phases, 
is  o-reater  than  w  +  2.  We  have  already  seen  (page  153)  that  it  is 
not  probable  that  this  is  ever  the  case. 

We  may,  however,  remark  that  in  a  certain  sense  an  infinitely  large 
fluid  mass  will  be  in  neutral  equilibrium  in  regard  to  the  formation 
of  the  substances,  if  such  there  are,  other  than  the  given  fluid,  for 
which  the  value  of  (133)  is  zero  (when  the  constants  are  so  deter- 
mined that  the  value  of  the  expression  is  zero  for  the  given  fluid, 
and  not  negative  for  any  substance)  ;  for  the  tendency  of  such  a  for- 
mation to  be  reabsorbed  will  diminish  indefinitely  as  the  mass  out  of 
which  it  is  formed  increases. 

When  the  substances  aS'j,  aS^,  .  .  .  S„  are  all  independently  vari- 
able components  of  the  given  mass,  it  is  evident  from  (86)  that  the 
conditions  that  the  value  of  (133)  shall  be  zero  for  the  mass  as  given, 
and  shall  not  be  negative  for  any  phase  of  the  same  components,  can 
only  be  fulfilled  when  the  constants  T,  P,  M^,  J/g,  .  .  .  M„  are  equal 
to  the  temperature,  the  pressure,  and  the  several  potentials  in  the  given 


J.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances.      159 

mass.  If  we  give  these  values  to  the  constants,  the  expression  (133) 
will  necessarily  have  the  value  zero  for  the  given  mass  and  we  shall  only 
have  to  inquire  whether  its  value  is  positive  for  all  other  phases. 
But  when  *S^j,  aS^o,  •  .  .  S„  are  not  all  independently  variable  compo- 
nents of  the  given  mass,  the  values  which  it  will  he  necessary  to  give 
to  the  constants  in  (133)  cannot  be  determined  entirely  from  the 
properties  of  the  given  mass ;  but  T  and  P  must  be  equal  to  its 
temperature  and  pressure,  and  it  will  be  easy  to  obtain  as  many  equa- 
tions connecting  J/,,  J/g,  .  .  .  M„  with  the  potentials  in  the  given 
mass  as  it  contains  independently  variable  components. 

When  it  is  not  possible  to  assign  such  values  to  the  constants  in 
(133)  that,  the  value  of  the  expression  shall  be  zero  for  the  given 
fluid,  and  either  zero  or  positive  for  any  phase  of  the  same  compo- 
nents, we  have  already  seen  (pages  129-134)  that  if  equilibrium 
subsists  without  passive  resistances  to  change,  it  must  be  in  virtue  of 
properties  which  are  peculiar  to  small  masses  surrounded  by  masses 
of  different  nature,  and  which  are  not  indicated  by  fundamental 
equations.  In  this  case,  the  fluid  will  necessarily  be  unstable,  if  we 
extend  this  term  to  embrace  all  cases  in  which  an  initial  disturbance 
confined  to  a  small  part  of  an  indefinitely  large  fluid  mass  will  cause 
an  ultimate  change  of  state  not  indefinitely  small  in  degree  through- 
out the  whole  mass.  In  the  discussion  of  stability  as  indicated  by 
fundamental  equations  it  will  be  convenient  to  use  the  term  in  this 
sense.* 

*  If  we  wish  to  know  the  stability  of  the  given  fluid  when  exposed  to  a  constant  tem- 
perature, or  to  a  constant  pressure,  or  to  both,  we  have  only  to  suppose  that  there  is 
enclosed  in  the  same  envelop  with  the  given  fluid  another  body  (which  cannot  combine 
with  the  fluid)  of  which  the  fundamental  equation  is  e  =  Ti],  or  e  =  —  Pv.  or  e  =  Ti] 
—  Pv.  as  the  case  may  be,  (Tand  P  denoting  the  constant  temperature  and  pressure, 
which  of  course  must  be  those  of  the  given  fluid,)  and  to  apply  the  criteria  of  page 
110  to  the  whole  system.  When  it  is  possible  to  assign  such  values  to  the  constants 
in  (133)  that  the  value  of  the  expression  shall  be  zero  for  the  given  fluid  and  positive 
for  every  other  phase  of  the  same  components,  the  value  of  (133)  for  the  whole  system 
will  be  less  when  the  system  is  in  its  given  condition  than  when  it  is  in  any  other. 
(Changes  of  form  and  position  of  the  given  fluid  are  of  course  regarded  as  immaterial.) 
Hence  the  fluid  is  stable.  When  it  is  not  possible  to  assign  such  values  to  the  con- 
stants that  the  value  of  (133)  shall  be  zero  for  the  given  fluid  and  zero  or  positive  for 
any  other  phase,  the  fluid  is  of  course  unstable.  In  the  remaining  case,  when  it  is 
possible  to  assign  such  values  to  the  constants  that  the  value  of  (133)  shall  be  zero 
for  the  given  fluid  and  zero  or  positive  for  every  other  phase,  but  not  without  the 
value  zero  for  some  other  phase,  the  state  of  equilibrium  of  the  fluid  as  stable 
or  neutral  wiU  be  determined  by  the  possibility  of  satisfying,  for  any  other  than 
the  given  condition  of  the  fluid,  equations  like  (134),  in  which,  however,  the  first 
or  the  second  or  both  are  to  be  stricken  out,  according  as  we  are  considering  the 


1 60      J.  W.  Gibhs — Equilihrium  of  Heterogeneoiis  Substances. 

In  determining  for  any  given  positive  values  of  T  and  P  and  any- 
given  values  whatever  of  3/,,  M^,  .  .  .  M„  whether  the  expression 
(133)  is  capable  of  a  negative  value  for  any  phase  of  the  components 
aSj,  aS'o,  .  .  .  /8„,  and  if  not,  whether  it  is  capable  of  the  value  zero 
for  any  other  phase  than  that  of  which  the  stability  is  in  question,  it 
is  only  necessary  to  consider  phases  having  the  temperature  T  and 
pressure  P.  For  we  may  assume  that  a  mass  of  matter  represented 
by  any  values  of  m^,  m^,  •  •  •  m„is  capable  of  at  least  one  state  ot 
not  unstable  equilibrium  (which  may  or  may  not  be  a  homogeneous 
state)  at  this  temperature  and  pressure.  It  may  easily  be  shown 
that  for  such  a  state  the  value  of  e  —  T?^-^  Pv  must  be  as  small  as 
for  any  other  state  of  the  same  matter.  The  same  will  therefore  be 
true  of  the  value  of  (133),  Therefore  if  this  expression  is  capable  of 
a  negative  value  for  any  mass  whatever,  it  will  have  a  negative  value 
for  that  mass  at  the  temperature  T  and  pressure  P.  And  if  this 
mass  is  not  homogeneous,  the  value  of  (133)  must  be  negative  for  at 
least  one  of  its  homogeneous  parts.  So  also,  if  the  expression  (133)  is 
not  capable  of  a  negative  value  for  any  phase  of  the  comj)onents, 
any  phase  for  which  it  has  the  value  zero  must  have  the  temperature 
T  and  the  pressure  P. 

It  may  easily  be  shown  that  the  same  must  be  true  in  the  limiting- 
cases  in  which  T=.0  and  P=:0.  For  negative  values  of  P,  (133) 
is  always  capable  of  negative  values,  as  its  value  for  a  vacuum  is  Pv. 

For  any  body  of  the  temperature  T  and  pressure  P,  the  expression 
(133)  may  by  (91)  be  reduced  to  the  form 

t,  —  J/i  m,  —  31^  m^  ...   —M„m„.  (135) 

We  have  already  seen  (pages  131,  132)  that  an  expression  like 
(133),  when  T,  P,  Jifj,  J/g,  .  .  .  J/„  and  v  have  any  given  finite 
values,  cannot  have  an  infinite  negative  value  as  applied  to  any  real 
body.  Hence,  in  determining  whether  (133)  is  capable  of  a  negative 
value  for  any  phase  of  the  components  aS'j,  S^,  .  .  .  jS„,  and  if  not, 
whether  it  is  capable  of  the  value  zero  for  any  other  phase  than  that 
of  which  the  stability  is  in  question,  we  have  only  to  consider  the 
least  value  of  which  it  is  capable  for  a  constant  value  of  v.  Any 
body  giving  this  value  must  satisfy  the  condition  that  for  constant 
volume 

de  -  T(h/  —  J/,  dm^  —  J/^  dot^  ...  —  3f„dm„^  0,      (136) 

stability  of  the  fluid  for  constant  temperature,  or  for  constant  pressure,  or  for  both. 
The  number  of  coexistent  phases  will  sometimes  exceed  by  one  or  two  the  number  of 
the  remaining  equations,  and  then  the  equilibrium  of  the  fluid  will  be  neutral  in 
respect  to  one  or  two  independent  changes. 


J.  W.  Gihhi< — Equilihrmia  of  Heterogeneous  Substances.      161 

or,  if  we  substitute  the  value  of  de  taken  from  equation  (86),  usinj^  sub- 
script a  .  .  .  g  for  the  quantities  rehiting  to  the  actual  components  of 
the  body,  and  subscript  h  .  .  .  k  for  those  relating  to  the  possible, 

t  dt]  4-  //„  dm,  .  .  .   +  M,  dm^  -\-  j.i^  dm^  .  .  .    -+-  jm  dm.^ 

—  Tdtf  -  31^  dm^  —  Jfs  f^^'h  •  •  •   -  M„dm„^  0.     (137) 

That  is,  the  temperature  of  the  body  must  be  equal  to  T,  and  the 
potentials  of  its  components  must  satisfy  the  same  conditions  as  if  it 
were  in  contact  and  in  equilibrium  with  a  body  having  potentials 
M^,  M2,  .  .  .  M„.  Therefore  the  same  relations  must  subsist  betAveeu 
//„...  //,„  and  M^  .  .  .  Jf„  as  between  the  units  of  the  corresponding 
substances,  so  that 

m,/.i,  .  .  .  ■j-m^ju„  =  m^  TJf^  .  .  .  +  m„  Jf„;  (138) 

and  as  we  have  by  (93) 

£  =  t}]^p  V  -h  IX,  m„  .  .  .  -\-  pij  m„  (139) 

the  expression  (133)  will  reduce  (for  the  body  or  bodies  for  which  it 
has  the  least  value  per  unit  of  volume)  to 

{F-p)v,  (140) 

the  value  of  which  will  be  positive,  null,  or  negative,  according  as 
the  value  of 

P  — jo  (141) 

is  positive,  null,  or  negative. 

Hence,  the  conditions  in  regard  to  the  stability  of  a  fluid  of  which  all 
the  ultimate  components  are  independently  variable  admit  a  very  sim- 
ple expression.  If  the  pressure  of  the  fluid  is  greater  than  that  of  any 
other  phase  of  the  same  components  which  has  the  same  temperature 
and  the  same  values  of  the  potentials  for  its  actual  components,  the 
fluid  is  stable  without  coexistent  phases  ;  if  its  pressure  is  not  as  great 
as  that  of  some  other  such  phase,  it  will  be  unstable ;  if  its  pressure  is 
as  great  as  that  of  any  other  such  phase,  but  not  greater  than  that 
of  every  other,  the  fluid  will  certainly  not  be  unstable,  and  in  all 
probability  it  will  be  stable  (when  enclosed  in  a  rigid  envelop  which 
is  impermeable  to  heat  and  to  all  kinds  of  matter),  but  it  will  be  one 
of  a  set  of  coexistent  phases  of  which  the  others  are  the  phases  which 
have  the  same  pressure. 

The  considerations  of  the  last  two  pages,  by  which  the  tests 
relating  to  the  stability  of  a  fluid  are  simplified,  apply  to  such  bodies 
as  actually  exist.  But  if  we  should  form  arbitrarily  any  equation  as 
a  fundamental  equation,  and  ask  whether  a  fluid  of  which  the  proper- 

Tbans.  Conn.  Acad.,  Vol.  III.  21  January,  1876. 


162      J.  W.  G-ibhs — EquUibriam  of  Heterogeneous  Substances. 

ties  were  given  by  that  equation  would  be  stable,  the  tests  of  stability- 
last  given  would  be  insufficient,  as  some  of  our  assumptions  might 
not  be  fulfilled  by  the  equation.  The  test,  however,  as  first  given 
(pages  156-159)  would  in  all  eases  be  sufficient. 

Stability  in  respect  to  Continuous  Changes  of  Phase. 

In  considering  the  changes  which  may  take  place  in  any  mass,  we 
have  already  had  occasion  to  distinguish  between  infinitesimal  changes 
in  existing  phases,  and  the  formation  of  entirely  new  phases.  A 
phase  of  a  fluid  may  be  stable  in  regard  to  the  former  kind  of  change, 
and  unstable  in  regard  to  the  latter.  In  this  case  it  may  be  capable 
of  continued  existence  in  virtue  of  properties  which  prevent  the  com- 
mencement of  discontinuous  changes.  But  a  phase  which  is  unstable 
in  regard  to  continuous  changes  is  evidently  incapable  of  permanent 
existence  on  a  large  scale  except  in  consequence  of  passive  resistances 
to  change.  We  will  now  consider  the  conditions  of  stability  in 
respect  to  continuous  changes  of  phase,  or,  as  it  may  also  be  called, 
stability  in  respect  to  adjacent  phases.  We  may  use  the  same  gen- 
eral test  as  before,  except  that  the  expression  (133)  is  to  be  applied 
only  to  phases  which  difier  infinitely  little  from  the  phase  of  which 
the  stability  is  in  question.  In  this  case  the  component  substances 
to  be  considered  will  be  limited  to  the  independently  variable  com- 
ponents of  the  fluid,  and  the  constants  M^,  M^.,  etc.  must  have  the 
values  of  the  potentials  for  these  components  in  the  given  fluid.  The 
constants  in  (133)  are  thus  entirely  determined  and  the  value  of  the 
expression  for  the  given  phase  is  necessarily  zero.  If  for  any  infi- 
nitely small  variation  of  the  phase,  the  value  of  (133)  can  become 
negative,  the  fluid  will  be  unstable ;  but  if  for  every  infinitely  small 
variation  of  the  phase  the  value  of  (133)  becomes  positive,  the  fluid 
will  be  stable.  The  only  remaining  case,  in  which  the  phase  can  be 
varied  without  altering  the  value  of  (133)  can  hardly  be  expected  to 
occur.  The  phase  concerned  woiild  in  such  a  case  have  coexistent 
adjacent  phases.  It  will  be  sufficient  to  discuss  the  condition  of  sta- 
bility (in  respect  to  continuous  changes)  without  coexistent  adjacent 
phases. 

This  condition,  which  for  brevity's  sake  we  Avill  call  the  condition 
of  stability,  may  be  written  in  the  form 

f "  _  t'  rf  -^p'v"  -  fA^'  m , "  .  .  .   -  /V  ni^'  >  0,  (142) 

in  which  the  quantities  relating  to  the  phase  of  which  the  stability  is 
in  question  are  distinguished  by  single  accents,  and  those  relating  to 


J.  W.  Gibbs — EqulUbrituti  of  Heterogeneous  tmbstances.      1G3 

the  other  phase  by  double  accents.  This  condition  is  by  (93)  equiva- 
lent to 

5"  _  t'  if  +p'  v"  -II,'  )>i,"  ...  —  //„' m„" 

—  f' +  «'?/—;/«'  +  /<, '/>i/  .   .   .   -!-//„' w„'>0,  (143) 

and  to 

^t'ff+pv"-,i,'m,"  .  .  .   -//:»?„" 
4.  t"  if  -  if  v"  +  1.1  ,"m^"  .  .  .   +  Mn"  mj'  >  0.  (144) 

The  condition  (143)  may  be  expressed  more  briefly  in  the  form 

z/f>  ^  J/;  —  ^>z/ti  + /<,  z/?Hj   .  .  .  -\-/.4„Jm„,  (145) 

if  we  use  the  character  J  to  signify  that  the  condition,  although 
relating  to  infinitesimal  differences,  is  not  to  be  interpreted  in  accord- 
ance with  the  usual  convention  in  respect  to  differential  equations 
with  neglect  of  infinitesimals  of  higher  orders  than  the  first,  but  is 
to  be  interpreted  strictly,  like  an  equation  between  finite  differences. 
In  fact,  when  a  condition  like  (145)  (interpreted  strictly)  is  satisfied 
for  infinitesimal  diffei'ences,  it  must  be  possible  to  assign  limits  within 
which  it  shall  hold  true  of  finite  differences.  But  it  is  to  be  remem- 
bered that  the  condition  is  not  to  be  applied  to  any  arbitrary  values 
of  Jyj,  z/u,  Zlm,,  .  .  .  Jnin,  but  only  to  such  as  are  determined  by  a 
change  of  phase.  (If  only  the  quantity  of  the  body  which  determines 
the  value  of  the  variables  should  vary  and  not  its  phase,  the  value  of 
the  first  member  of  (145)  would  evidently  be  zero.)  We  may  free 
ourselves  from  this  limitation  by  making  v  constant,  which  will 
cause  the  term  —  p  Av  to  disappear.  If  we  then  divide  by  the  con- 
stant V,  the  condition  will  become 

in  which  form  it  will  not  be  necessary  to  regard  v  as  constant.  As 
we  may  obtain  from  (86) 

V  V  V  V 

we  see  that  the  stability  of  any  phase  in  regard  to  continuous  changes 
depends  ujion  the  same  conditions  in  regard  to  the  second  and  higher 
differential  coefficients  of  the  density  of  energy  regarded  as  a  function 
of  the  density  of  entropy  and  the  densities  of  the  several  components^ 
which  would  make  the  density  of  energy  a  minimum,  if  the  necessary 
conditions  in  regard  to  the  first  differential  coefficients  were  fulfilled. 
When   //=  1,  it  may  be  more  convenient  to  regard  m  as  constant 


164     J.   W.  Gihhs — Equilibrium  of  Heterogeneous  Substances. 

in  (145)  than  v.  Regarding  m  a  constant,  it  appears  that  the  stability 
of  a  phase  depends  upon  the  same  conditions  in  regard  to  the  second 
and  higher  differential  coefficients  of  the  energy  of  a  unit  of  mass 
regarded  as  a  function  of  its  entropy  and  volume,  which  would  make 
the  energy  a  minimum,  if  the  necessary  conditions  in  regard  to  the 
first  differential  coefficients  were  fulfilled. 

The  formula  (144)  expresses  the  condition  of  stability  for  the  phase 
to  which  t',  p\  etc.  relate.  But  it  is  evidently  the  necessary  and 
sufficient  condition  of  the  stability  of  all  phases  of  certain  kinds  of 
matter,  or  of  all  phases  within  given  limits,  that  (144)  shall  hold  true 
of  any  two  infinitesimally  diffi^ring  phases  within  the  same  limits,  or, 
as  the  case  may  be,  in  general.  For  the  purpose,  therefore,  of  such 
collective  determinations  of  stability,  we  may  neglect  the  distinction 
between  the  two  states  compared,  and  write  the  condition  in  the  form 

—  1/ ^t-\-v  ^p —  m^  J/4^   .   .  .    —m„JjJ„>0,  (148) 

or 

Comparing  (98),  we  see  that  it  is  necessary  and  sufficient  for  the  sta- 
bility in  regard  to  continuous  changes  of  all  the  phases  within  any 
given  limits,  that  within  those  limits  the  same  conditions  should  be 
fulfilled  in  respect  to  the  second  and  higher  differential  coefficients  of 
the  pressure  regarded  as  a  function  of  the  temperature  and  the  sev- 
eral potentials,  which  would  make  the  pressure  a  minimum,  if  the 
necessary  conditions  witb  i-espect  to  the  first  difierential  coefficients 
were  fiilfilled. 

By  equations  (87)  and  (94),  the  condition  (142)  may  be  brought  to 
the  form 

->-?/■'  ~  t'  if  —p'  v'  -\-  /.ii'  m^'    .  .  .   -\.  ^(J  m„'>0.         (150) 

For  the  stability  of  all  phases  within  any  given  limits  it  is  necessary 
and  sufficient  that  within  the  same  limits  this  condition  shall  hold 
true  of  any  two  phases  which  differ  infinitely  little.  This  evidently 
requires  that  when  v'  =.  d",  m^'  =  iii  ^\  .  .  .   in„'  =  rnj\ 

f  ~'/'+{t"  -t'),/'>0;  (151) 

and  that  when  t'  —  t" 

f  +P'  '^"  -  /<  1 '  >/*i"  .   •  .    4-  /'„'  mj' 
-  f  ~  P' ''' -\- M i  ">  i'  ■  ■  ■    +/'„'/>?„' >U.  (152) 

These  conditions  may  be  written  in  the  form 


J.  W.  Gihhs — Equilihrium  of  Heterogeneous  Substances.      165 

[JV'4-//Z/«]„,^<0,  (153) 

{Aip+pAv~i.i^Jm^   .   .  .    -/<„Jw„],>0,  (154) 

in  which  the  subscript  letters  indicate  the  quantities  which  are  to  be 
resjarded  as  constant,  m  standing  for  all  the  quantities  m,  .  .  .  m„. 
If  these  conditions  hold  true  within  any  given  limits,  (150)  will  also 
hold  true  of  any  two  iniinitesimally  differing  phases  within  the  same 
limits.     To  prove  this,  we  will  consider  a  third  phase,  determined 

by  the  equations 

t"'  =  t',  (155) 

and 

v"'  =  v",     m/"  =  m,",     .     .     .     m„"'  =  m„".  (156) 

Now  by  (153), 

r'-'/'"+(«"'-«")  v"<o;  (157) 

and  by  (154), 

- //''     —p'v'   H-/<,'//^i'     .    .    .    4- yU„' //<„'>  0.  (158) 

Hghcg 

'  r  +  t"   rf+p'v"'-fx,'m,"'  .  .   .    -yu„'m„"' 

_^/  ^t'"  if  -p'v'    +j.{^'m,'  .  .  .    +jj„'m„'>0,       (159) 

which  by  (155)  and  (156)  is  equivalent  to  (150).  Therefore,  the  con- 
ditions (153)  and  (154)  in  respect  to  the  phases  within  any  given 
limits  are  necessary  and  sufficient  for  the  stability  of  all  the  phases 
within  those  limits.  It  will  be  observed  that  in  (153)  we  have  the 
condition  of  thermal  stability  of  a  body  considered  as  unchangeable 
in  composition  and  in  volume,  and  in  (154),  the  condition  of  mechan- 
ical and  chemical  stability  of  the  body  considered  as  maintained  at  a 
constant  temperature.     Comparing  equation    (88),  we  see  that   the 

condition  (153)  will  be  satisfied,  if  -^  <0,  i.  e.,  if --^  or  #-^  (the  spe- 
cific heat  for  constant  volume)  is  positive.  When  n=.  1,  i.  e.,  when 
the  composition  of  the  body  is  invariable,  the  condition  (154)  will 
evidently  not  be  altered,  if  we  regard  m  as  constant,  by  which  the 
condition  will  be  reduced  to 

[z/z/'-fjo  J4,,„>0.  (160) 

d^  lb  dp 

This  condition  will  evidently  be  satisfied  if  3-^  ^^^  i-  *?-,  if  -7-  or 

_  rf^JL   (the   elasticity  for   constant  temperature)  is  positive.     But 

dv 
when  7i>  1,  (154)  may  be  abbreviated  more  symmetrically  by  making 
v  constant. 

Again,  by  (91)   and  (96),  the  condition    (142)   may  be  brought  to 
the  form 


106      J.  W.  Gihhs — Equillhrhim  of  Heterogeneous  Substances. 

■c^"  +  t"  if  -p"  v"  -  fx.'m,"  .  .  .    -  //„'  m„" 
-t,'  -t'lf  ->rp'v"  +fi,'m^'  .  .  .    +//„'m„'>0.  (161) 

Therefore,  for  the  stability  of  all  phases  within  any  given  limits  it  is 
necessary  and  sufficient  that  within  the  same  limits 

[JC  + //^«  -  v44„<0,  (162) 

and 

[A^-  fx^Am^   .  .   .    -<-yW„Jm„],,>0,  (.163) 

as  may  easily  be  proved  by  the  method  used  with  (153)  and  (154). 
The  first  of  these  formulae  expresses  the  thermal  and  mechanical  con- 
ditions of  stability  for  a  body  considered  as  michangeable  in  compo- 
sition, and  the  second  the  conditions  of  chemical  stability  for  a  body 
considered  as  maintained  at  a  constant  temperature  and  pressure.  If 
'/i=  1,  the  second  condition  falls  away,  and  as  in  this  case  ?  =  m/<, 
condition  (162)  becomes  identical  with  (148). 

The  foregoing  discussion  will  serve  to  illustrate  the  relation  of  the 
general  condition  of  stability  in  regard  to  continuous  changes  to 
some  of  the  principal  forms  of  fundamental  equations.  It  is  evident 
that  each  of  the  conditions  (146),  (149),  (154),  (162),  (163)  involve 
in  general  several  particular  conditions  of  stability.  We  will  now 
give  our  attention  to  the  latter.     Let 

fp  ■=  €  —  t' 7/ +p' V  —  ^i^' )n^   .  .  .   — /<„'«<„,  (164) 

the  accented  letters  referring  to  one  phase  and  the  unaccented  to 
another.  It  is  by  (142)  the  necessary  and  sufficient  condition  of  the 
stability  of  the  first  phase  that,  for  constant  values  of  the  quantities 
relatino-  to  that  phase  and  of  v,  the  value  of  $  shall  be  a  minimiim 
when  the  second  phase  is  identical  with  the  first.  Diflerentiating 
(164),  we  have  by  (86) 

d^  =  {t  -  t')  ch]  —  {p  —jo')  dn  +  (//j  —  /i/)  dm^ 

...    -  (Af„  -  /^„')f?m„.      (165) 

Therefore,  the  above  condition  requires  that  if  we  regard  v,m^,  .  .  . 
m„  as  having  the  constant  values  indicated  by  accenting  these  letters, 
t  shall  be  an  increasing  function  of  ;/,  when  the  variable  phase  differs 
sufficiently  little  from  the  fixed.  But  as  the  fixed  phase  may  be  any 
one  within  the  limits  of  stability,  t  must  be  an  increasing  function  of 
//  (within  these  limits)  for  any  constant  values  of  v,  'm^,  .  .  .  m,^. 
This  condition  may  be  written 

(j4J         ^^-  (^^^) 

X^ijlv,  nit,  .  .  .  m„ 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.      167 

When  this  condition  is  satisfied,  the  value  of  ^,  foi*  any  ijiven  vahies 
oft?,  wij,  .  .  .  ;/^„  will  be  a  minimum  when  t-=.t'.  And  therefore,  in 
applying  the  general  condition  of  stability  relating  to  the  value  of 
<^,  we  need  only  consider  the  phases  for  which  t  =  t'. 

We  see  again  by  (165)  that  the  general  condition  requires  that 
if  we  regard  ^,  y,  ni^.,  .  .  .  m„  as  having  the  constant  values  indicated 
by  accenting  these  letters,  //j  shall  be  an  increasing  function  of  m,, 
when  the  variable  phase  difters  sufficiently  little  from  the  fixed.  But 
as  the  fixed  phase  may  be  any  one  within  the  limits  of  stability,  /.i , 
must  be  an  increasing  function  of  m  j  (within  these  limits)  for  any 
constant  values  of  ^,  v,  mg,  .  .  .  m„.     That  is, 

(i^)  >0-  (16V) 

When  this  condition  is  satisfied,  as  well  as  (166),  ^  will  have  a  min- 
imum value,  for  any  constant  values  of  v,  m^^  .  •  .  ?/*„,  when  t=it' 
and  yu,  =  ///;  so  that  in  applying  the  general  condition  of  stability 
we  need  only  consider  the  phases  for  which  t-=.t'  and  //j  =  yu/. 

In  this  way  we  may  also  obtain  the  follov\^ing  particular  conditions 
of  stability  : 

(4^)  >0,  (168) 

\nm^lt^  w,  m,,  ma,  .  .  .  ??i„ 

(4^\  >0.  (169) 

\Amjt,  V,  mi,  .  .  .  m„_, 

When  the  7i-\-  1  conditions  (166)-(169)  are  all  satisfied,  the  value 
of  ^,  for  any  constant  value  of  v,  will  be  a  minimum  when  the  tem- 
perature and  the  potentials  of  the  variable  phase  are  equal  to  those 
of  the  fixed.  The  pressures  will  then  also  be  equal  and  the  phases 
will  be  entirely  identical.  Hence,  the  general  condition  of  stability 
will  be  completely  satisfied,  when  the  above  particular  conditions  are 
satisfied. 

From  the  manner  in  which  these  particular  conditions  have  been 
derived,  it  is  evident  that  we  may  interchange  in  them  a/,  m^,  .  .  .  m„ 
in  any  way,  provided  that  we  also  interchange  in  the  same  way 
^, //,,  .  .  .  //„.  In  this  way  we  may  obtain  different  sets  of  n -\-  1 
conditions  which  are  necessary  and  sufficient  for  stability.  The  quan- 
tity V  might  be  included  in  the  first  of  these  lists,  and  ~  p  in  the 
second,  except  in  cases  w^hen,  in  some  of  the  phases  considered,  the 
entropy  or  the  quantity  of  one  of  the  components  has  the  value  zero. 


168      J.  W.  Gihbs — Equilibrium  of  Heterogeneous  Substances. 

Then  the  condition  that  that  quantity  shall  be  constant  would  create 
a  restriction  upon  the  variations  of  the  phase,  and  cannot  be  substi- 
tuted for  the  condition  that  the  volume  shall  be  constant  in  the  state- 
ment of  the  general  condition  of  stability  relative  to  the  minimum 
value  of  0. 

To  indicate  more  distinctly  all  these  particular  conditions  at  once, 
we  observe  that  the  condition  (144),  and  therefore  also  the  condition 
obtained  by  interchanging  the  single  and  double  accents,  must  hold 
true  of  any  two  infinitesimally  difiering  phases  within  the  limits  of 
stability.     Combining  these  two  conditions  we  have 

i^t"  -  t')  [rf  -  rf)  -  {p"  -p')  W  -  ^') 

+  (/^i"  -  /^i')  (^i"  -  '-'^x)  •  •  '   (/^""  -  Z^"')  «'-O>0,  (170) 

which  may  be  written  more  briefly 

AtAr]  —  ApAv-{- Jf^^Am^  .  .  .  +J//„Jm„>0.         (IVI) 

This  must  hold  true  of  any  two  infinitesimally  differing  phases  within 
the  limits  of  stability.  If,  then,  we  give  the  value  zero  to  one  of  the 
differences  in  every  term  except  one,  but  not  so  as  to  make  the  phases 
completely  identical,  the  values  of  the  two  differences  in  the  remain- 
ing term  will  have  the  same  sign,  except  in  the  case  of  Ap  and  Av, 
which  will  have  opposite  signs.  (If  both  states  are  stable  this  will 
hold  true  even  on  the  limits  of  stability.)  Therefore,  within  the 
limits  of  stability,  either  of  the  two  quantities  occurring  (after  the 
sign  A)  in  any  term  of  (IVI)  in  an  increasing  function  of  the  other, 
— except  p  and  v,  of  which  the  opposite  is  true, — when  we  regard  as 
constant  one  of  the  quantities  occurring  in  each  of  the  other  terms, 
but  not  such  as  to  make  the  phases  identical. 

If  we  write  <^?  for  A  in  (166)-(169),  we  obtain  conditions  which  are 
always  sufficient  for  stability.  If  we  also  substitute  ^  for  >,  we 
obtain  conditions  which  are  necessary  for  stability.  Let  us  consider 
the  form  which  these  conditions  will  take  when  ?/,  v,  m,,  .  .  .  m.„  are 
regarded  as  independent  variables.     When  dv  =  0,  we  shall  have 

dt  dt  ,     dt    ^ 

at=i—  drj  -\-  - —  dm ,   .  .  .  +  -^ —  dm. 
dt]  dm^  dm^ 

d\x.—^-^di]-\-^^dm.   .  .  .   +  4^dm„   [  .,^„, 

^*        d}]  dm^        ^  dm„  \  (172) 

_  d^„  ,     ,    dfA^   ,  c?w_  , 

du„=z  -^-dn  -{--z — dm,   .  .  .    -\--~^dm„ 
dt]  dm^^        ^  dm„ 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.      169 
Let  us  write  i?„+i  for  the  determinant  of  the  order  n  +  1 


d'^e 

d'-e 

d-^e 

dtf 

dm^  dr] 

dm^drj 

d-^e 

d^e 

d^e 

dij  dm  J 

dm^^ 

diii^dm 

d^e 

d^E 

d^e 

d)]  dm^ 

dm.  dm„ 

dm„^ 

(173) 


of  which  the  constituents  are  by  (86)  the  same  as  the  coefficients  in 
equations  (1*72),  and  i?„,  B^_-^,  etc.  for  the  minors  obtained  by  erasing 
the  hist  column  and  row  in  the  original  determinant  and  in  the  minors 
successively  obtained,  and  R^  for  the  last  remaining  constituent. 
Then  if  dt,  dju^,  .  .  .  djn„-i,  and  dv  all  have  the  value  zero,  we  have 
by  (172) 

Ji„  dj.i„  =  i?„+i  drji„,  (174) 

that  is. 


/d/Jr,  \ 

\dinjt,  v,/x,, 


/""— 1 


In  like  manner  we  obtain 


(d^„_i\ 

\dm„_Jt,v,fii, 


/"»-2>  »»„ 


RZ. 


(175) 


(176) 


etc. 


Therefore,  the  conditions  obtained  by  writing  d  for  A  in  (166)-(169) 
are  equivalent  to  this,  that  the  determinant  given  above  with  the  n 
minors  obtained  from  it  as  above  mentioned  and  the  last  remaining 

d^  £ 
constituent  -y—  shall  all  be  positive.  Any  phase  for  which  this  con- 
dition is  satisfied  will  be  stable,  and  no  phase  will  be  stable  for 
which  any  of  these  quantities  has  a  negative  value.  But  the  condi- 
tions (166)-(169)  will  remain  valid,  if  we  interchange  in  any  way 
77,  w^i,  .  .  .  m„  (with  corresponding  interchange  of  t,  ^t^,  .  .  .  /.i„). 
Hence  the  order  in  which  we  erase  successive  columns  with  the  cor- 
responding rows  in  the  determinant  is  immaterial.  Therefore  none 
of  the  minors  of  the  determinant  (173)  which  are  formed  by  erasing 
corresponding  rows  and  columns,  and  none  of  the  constituents  of  the 
principal  diagonal,  can  be  negative  for  a  stable  phase. 

We  will  now  consider  the  conditions  Avhich  characterize  the  limits 
of  stability  (i.  e.,  the  limits  which  divide  stable  from  unstable  phases) 

Trans.  Conn.  Acad.,  Vol.  III.  22  January,  1876. 


IVO      J.  W.  Gibhs — EquiUhrium  of  Heterogeneous  Substances. 

with  respect  to  continuous  changes.*  Here,  evidently,  one  of  the 
conditions  (166)-(169)  must  cease  to  hold  true.  Therefore,  one  of  the 
differential  coefficients  formed  by  changing  J  into  d  in  the  first  mem- 
bers of  these  conditions  must  have  the  value  zero.  (That  it  is  the 
numerator  and  not  the  denominator  in  the  differential  coefficient 
which  vanishes  at  the  limit  appears  from  the  consideration  that  the 
denominator  is  in  each  case  the  differential  of  a  quantity  which  is 
necessarily  capable  of  progressive  variation,  so  long  at  least  as  the 
phase  is  capable  of  variation  at  all  under  the  conditions  expressed 
by  the  subscript  letters.)  The  same  will  hold  true  of  the  set  of  dif- 
ferential coefficients  obtained  from  these  by  interchanging  in  any 
way  rj,  m^,  .  .  .  m„,  and  simultaneously  interchanging  t,  j.i^,  .  .  .  /J„ 
in  the  same  way.  But  we  may  obtain  a  more  definite  result  than  this. 
Let  us  give  to  rj  or  t,  to  m^  or  j.i^,  ..  .  to  m„_j  or  /y„_i,  and  to  v, 
the  constant  values  indicated  by  these  letters  when  accented.     Then 

by  (165) 

d^=iMu  -  l<)dm,.  {Ill) 

Now 

""-"•'=(,17.) '('"•-'"•')  (^'«> 

approximately,  the  differential  coefficient  being  interpreted  in  accord- 
ance with  the  above  assignment  of  constant  values  to  certain  vari- 
ables, and  its  value  being  determined  for  the  phase  to  which  the 
accented  letters  refer.     Therefore, 


and 


d^  =  1^^]  {m„  -  m„')  dm,,,  (179) 

^  =  -m^y(m„-m„')^.  (180) 

The  quantities  neglected  in  the  last  equation  are  evidently  of  the 
same  order  as  (v;?„  —  w^„')^.  Now  this  value  of  ^  will  of  course  be 
different  (the  differential  coefficient  having  a  different  meaning) 
according  as  we  have  made  //  or  t  constant,  and  according  as  we  have 
made  m^  or  /^^  constant,  etc. ;  but  since,  within  the  limits  of  stability, 
the  value  of  <?,  for  any  constant  values  of  «?„  and  ?j,  Avill  be  the  least 
when  t^p,  1^1  .  .  .  //„_i  have  the  values  indicated  by  accenting  these 
letters,  the  value  of  the  differential  coefficient  will  be  at  least  as  small 


*  The  limits  of  stability  with  respect  to  discontinuous  changes  are  formed  by  phases 
which  are  coexistent  with  other  phases.  Some  of  the  properties  of  such  phases  have 
already  been  considered.     See  pages  152-156. 


J.  W.  Gibhs — Equilihrmm  of  Heterogeneous  l^ubstuHces.      171 

when  we  give  these  variables  these  constant  values,  as  when  we 
adopt  any  other  of  the  suppositions  mentioned  above  in  re<^ard  to  the 
quantities  remaining  constant.  And  in  all  these  relations  we  may- 
interchange  in  any  way  //,  >«,,  .  .  .  «?„,  if  we  intercliange  in  the  same 
way  t,  p(^,  .  .  .  i.i„.  It  follows  that,  within  the  limits  of  stability, 
when  we  choose  for  anj^  one  of  the  differential  coefficients 

dt       dii  J  c///„ 

d7f     dw^;  '  '  '    dm„  (^^1) 

the  quantities  following  the  sign  d  in  the  numerators  of  the  others 
together  with  v  as  those  which  are  to  remain  constant  in  diiferentia- 
tion,  the  value  of  the  differential  coefficient  as  thus  determined  will 
be  at  least  as  small  as  when  one  or  more  of  the  constants  in  differen- 
tiation are  taken  from  the  denominators,  one  being  still  taken  from 
each  fraction,  and  v  as  before  being  constant. 

Now  we  have  seen  that  none  of  these  differential  coefficients,  as 
determined  in  any  of  these  ways,  can  have  a  negative  value  within 
the  limit  of  stability,  and  that  some  of  them  must  have  the  value  zero 
at  that  limit.  Therefore,  in  virtue  of  the  relations  just  established 
one  at  least  of  these  differential  coefficients  determined  by  considerino- 
constant  the  quantities  occurring  in  the  numeratoi-s  of  the  others 
together  with  v,  will  have  the  value  zero.  But  if  one  such  has  the 
value  zero,  all  such  will  in  general  have  the  same  value.     For  if 

for  example,  has  the  value  zero,  we  may  change  the  density  of  the 
component  S„  without  altering  (if  we  disregard  infinitesimals  of 
higher  orders  than  the  first)  the  temperature  or  the  potentials,  and 
therefore,  by  (98),  without  altering  the  pressure.  That  is,  we  may 
change  the  phase  without  altering  any  of  the  quantities  t,j),  /<j,  ,  .  . 
/,/„,  (In  other  words,  the  phases  adjacent  to  the  limits  of  stability 
exhibit  apj^roncimateli/  the  relations  characteristic  of  neutral  equili- 
brium.) Now  this  change  of  phase,  which  changes  the  density  of 
one  of  the  components,  will  in  general  change  the  density  of  the 
others  and  the  density  of  entropy.  Therefore,  all  the  other  differen- 
tial coefficients  formed  after  the  analogy  of  (182),  i,  e.,  formed  from 
the  fractions  in  (181)  by  taking  as  constants  for  each  the  quantities  in 
the  numerators  of  the  others  together  with  u,  will  in  general  have 
the  value  zero  at  the  limit  of  stability.  And  the  relation  which 
characterizes  the  limit  of  stability  may  be  expressed,  in  general,  by 
setting  any  one  of  these  differential  coefficients  equal  to  zero.     Such 


172       J.  W.  Gibbs — Equilibrium  of  Heterogenous  Substances. 

an  equation,  when  tlie  fundamental  eqnation  is  known,  may  be 
reduced  to  the  form  of  an  equation  between  the  independent  variables 
of  the  fundamental  equation. 

Again,  as  the  determinant  (IVS)  is  equal  to  the  product  of  the 
differential  coefficients  obtained  by  writing  d  for  A  in  the  first 
members  of  (166)-(169),  the  equation  of  the  limit  of  stability  may  be 
expressed  by  setting  this  determinant  equal  to  zero.  The  form  of 
the  differential  equation  as  thus  expressed  will  not  be  altered  by  the 
interchange  of  the  expressions  ;/,  «?.j,  .  .  .  »?„,  but  it  will  be  altered 
by  the  substitution  of  v  for  any  one  of  these  expressions,  which  will 
be  allowable  whenever  the  quantity  for  which  it  is  substituted  has 
not  the  value  zero  in  any  of  the  phases  to  which  the  formula  is  to  be 
applied. 

The  condition  formed  by  setting  the  expression  (182)  equal  to  zero 
is  evidently  equivalent  to  this,  that 


that  is,  that 


3=0,  (183) 


or  by  (98),  if  we  regard  ^,  //j,  ...  /^„  as  the  independent  variables, 

(It?)  =  '"^  <'««> 

In  like  manner  we  may  obtain 


(186) 


d^p  d^p  d^p 

^-"'  ^?  =  "'-  •  •  diAZ7'  =  '^- 

Any  one  of  these  equations,  (185),  (186),  may  be  regarded,  in  gen- 
eral, as  the  equation  of  the  limit  of  stability.  We  may  be  certain 
that  at  every  phase  at  that  limit  one  at  least  of  these  equations  will 
hold  true. 

GEOMETRICAL    ILLITSTRATIONS. 

Surfaces  in  tchich  the  Composition  of  the  Body  represented  is 

Constant. 
In  vol.  ii,  p.  382,  of  the  Trans.  Conn.  Acad.,  a  method  is  described  of 
representing  the  thermodynamic  properties  of  substances  of  invariable 
composition  by  means  of  surf^xces.     The  volume,  entropy,  and  energy 


J.  ^V.  (xibhs — Equilibrium  of  Heterogeneous  ISuhsfances.      17;5 

of  a  constant  quantity  of  a  substance  are  represented  by  rectangular 
co-ordinates.  This  method  corresponds  to  the  first  kind  of  limda- 
raental  equation  described  on  pages  140-144.  Any  other  kind  of 
fundamental  equation  for  a  substance  of  invariable  composition  will 
suggest  an  analogous  geometrical  method.  Thus,  if  we  make  m  con- 
stant, the  variables  in  any  one  of  the  sets  (99)-(103)  are  reduced  to 
three,  which  may  be  represented  by  rectangular  co-ordinates.  This 
will,  however,  afford  but  four  different  methods,  for,  as  has  already 
(page  150)  been  observed,  the  two  last  sets  are  essentially  equivalent 
when  n  ■=  \. 

The  method  described  in  the  preceding  volume  has  certain  advan- 
tages, especially  for  the  purposes  of  theoretical  discussion,  but  it  may 
often  be  more  advantageous  to  select  a  method  in  which  the  proper- 
ties represented  by  tM'o  of  the  co-ordinates  shall  be  such  as  best  serve 
to  identify  and  describe  the  different  states  of  the  substance.  This 
condition  is  satisfied  by  temperature  and  pressiire  as  well,  perhaps,  as 
by  any  other  properties.  We  may  represent  these  by  two  of  the 
co-ordinates  and  the  potential  by  the  third.  (See  page  143.)  It 
will  not  be  overlooked  that  there  is  the  closest  analogy  between  these 
three  quantities  in  respect  to  their  parts  in  the  general  theory  of 
equilibrium.  ( A  similar  analogy  exists  between  volume,  entropy,  and 
energy.)  If  we  give  m  the  constant  value  unity,  the  third  co-ordinate 
will  also  represent  C,  which  then  becomes  equal  to  /<. 

Comparing  the  two  methods,  we  observe  that  in  one 

v  =  x,     i]  —  y,     €  =  z,  (187) 

dz  dz  ^  dz  dz  ,^^^ 

and  in  the  other 

t-z.x^    p=-y,     i.i^'C,z=.z,  (189) 

dz  dz  dz  dz  ,       ^ 

uX  clx 

Now  ^—  and  ^—  are  evidently  determined  by  the  inclination  of  the 
dx  dy 

(Txi  (XX 

tangent  plane,  and  z  —  -^  x  —  -^y  is  the  segment  which  it  cuts  ofi" 

on  the  axis  of  Z.  The  two  methods,  therefore,  have  this  reciprocal 
relation,  that  the  quantities  represented  in  one  by  the  position  of  a 
point  in  a  surface  are  represented  in  the  other  by  the  position  of  a 
tangent  plane. 


1 74      J.  W.  Glbbs — EqmUhriuiin  of  Heterogeneous  Substances. 

The  surfaces  detined  by  equations  (187)  and  (189)  may  be  distin- 
guished as  the  v-7]-e  surface,  and  the  t-2>'C  surface,  of  the  substance  to 
which  they  relate. 

In  the  t-p-'C  surface  a  line  in  which  one  part  of  the  surface  cuts 
another  represents  a  series  of  pairs  of  coexistent  states.  A  point 
through  whicli  pass  three  different  parts  of  the  surface  represents  a 
triad  of  coexistent  states.  Through  such  a  point  will  evidently  pass 
the  three  lines  formed  by  the  intersection  of  these  sheets  taken  two 
by  two.  The  perpendicular  projection  of  these  lines  upon  the  i>t 
plane  will  give  the  curves  which  have  recently  been  discussed  by  Pro- 
fessor J.  Thomson.*  These  curves  divide  the  space  about  the  projec- 
tion of  the  triple  point  into  six  parts  which  may  be  distinguished  as 
follows :  Let  C^'^^,  C^^',  ^^*-'  denote  the  three  ordinates  determined  for 
the  same  values  of  p  and  t  by  the  three  sheets  passing  through  the 
triple  point,  then  in  one  of  the  six  spaces 

^(n<Ki)<^(s,^  (191) 

in  the  next  space,  separated  from  the  fornier  by  the  line  for  which 

^(n<^(S)<^(z)^  (192) 

in  the  third  space,  separated  from  the  last  by  the  line  for  which 

^(Sj<^(n^^W  (193) 

in  the  fourth                             ?(«>  <  ?(^)  <  C^''\  (194) 

in  the  fifth                                  C^^>  <  tS^^  <  ?(^),  (195) 

in  the  sixth                               C<^>  <  ?(^)  <  ?(«>.  (196) 

The  sheet  which  gives  the  least  values  of  'C,  is  in  each  case  that  which 
represents  the  stable  states  of  the  substance.  From  this  it  is  evident 
that  in  passing  around  the  projection  of  the  triple  point  we  pass 
through  lines  representing  alternately  coexistent  stable  and  coexistent 
unstable  states.  But  the  states  represented  by  the  intermediate 
values  of  ?  may  be  called  stable  relatively  to  the  states  represented 
by  the  highest.  The  differences  C^^^  —  ^^'>,  etc.  represent  the  amount 
of  woi"k  obtained  in  bringing  the  substance  by  a  reversible  process 
from  one  to  the  other  of  the  states  to  which  these  quantities  relate, 
in  a  medium  having  the  temperature  and  pressure  common  to  the 
two  states.  To  illustrate  such  a  process,  we  may  suppose  a  plane 
perpendicular  to  the  axis  of  temperature  to  pass  through  the  points 

*  See  the  Keports  of  the  British  Association  for  1871  and  1872  ;  and  Philosophical 
Magazine,  vol.  xlvii.  (1874),  p.  447. 


J.  W.  Gibhs—Equilibrlaui  of  Ileterofjeneous  SuhsUmres.       175 

representing  tlie  two  states.  This  will  in  genorul  cut  tlie  double  line 
formed  by  the  two  sheets  to  which  the  symbols  [L)  and  (  T^)  refer. 
The  intersections  of  the  plane  with  the  two  sheets  will  connect  the 
double  point  thus  determined  with  the  i)oints  representino-  the 
initial  and  linal  states  of  the  process,  and  thus  form  a  reversible  path 
for  the  body  between  those  states. 

The  geometrical  relations  which  indicate  tlie  stability  of  any  state 
may  be  easily  obtained  by  applying  the  principles  stated  on  pp.  156  ff. 
to  the  case  in  which  there  is  but  a  single  component.  The  expres- 
sion (133)  as  a  test  of  stability  will  reduce  to 

e  -t'T/-\-p'v  -  /.I'm,  (197) 

the  accented  letters  referring  to  the  state  of  which  the  stability  is  in 
question,  and  the  unaccented  letters  to  any  other  state.  If  we  con- 
sider the  quantity  of  matter  in  each  state  to  be  unity,  this  expression 
may  be  reduced  by  equations  (91)  and  (96)  to  the  form 

^-l''+(«-0v-(7^-/>V,  (198) 

which  evidently  denotes  the  distance  of  the  point  {t',p',  t')  below  the 
tangent  plane  for  the  point  {t,  p,  t),  measured  parallel  to  the  axis  of  'Q. 
Hence  if  the  tangent  plane  for  every  other  state  passes  above  the 
point  representing  any  given  state,  the  latter  will  be  stable.  If  any 
of  the  tangent  planes  pass  below  the  point  rejjresenting  the  given 
state,  that  state  will  be  unstable.  Yet  it  is  not  always  necessary  to 
consider  these  tangent  planes.  For,  as  has  been  observed  on  page- 
160,  we  may  assume  that  (in  the  case  of  any  real  substance)  there 
will  be  at  least  one  not  unstable  state  for  any  given  temperature  and 
pressure,  except  when  the  latter  is  negative.  Therefore  the  state 
represented  by  a  point  in  the  surface  on  the  positive  side  of  the 
plane  jo=  0  will  be  unstable  only  when  there  is  a  point  in  the  surface 
for  which  t  and  p  have  the  same  values  and  C  a  less  value.  It  follows 
from  what  has  been  stated,  that  where  the  surface  is  doubly  convex 
upwards  (in  the  direction  in  which  'C  is  measured)  the  states  repre- 
sented will  be  stable  in  respect  to  adjacent  states.  This  also  appears 
directly  from  (162).  But  where  the  surface  is  concave  upwards  in 
either  of  its  principal  curvatures  the  states  represented  will  be  unsta- 
ble in  respect  to  adjacent  states. 

When  the  number  of  component  substances  is  greater  than  unity, 
it  is  not  possible  to  represent  the  fundamental  equation  by  a  single 
surface.  We  have  therefore  to  consider  how  it  may  be  represented 
by  an  infinite  number  of  surfaces.  A  natural  extension  of  either  of 
the  methods  already  described  will  give  us  a  series  of  surfaces  in 


176     J.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 

which  every  one  is  the  v-7]-e  surface,  or  every  one  the  t-p-l  surface  for 
a  body  of  constant  composition,  the  proportion  of  the  components 
varying  as  we  pass  from  one  surface  to  another.  But  for  a  simultaneous 
view  of  the  properties  which  are  exhibited  by  compounds  of  two  or 
three  comj^onents  without  change  of  temperature  or  pressure,  we  may 
more  advantageously  make  one  or  both  of  the  quantities  t  or  p  con- 
stant in  each  surface. 

Surfaces  and  Curves  in  tchich  the  Composition  of  the  Body  repre- 
sented is  Variable  and  its  Temperature  and  Pressure  are  Constant. 

When  there  are  three  components,  the  position  of  a  point  in  the 
J^I^plane  may  indicate  the  composition  of  a  body  most  simply,  per- 
haps, as  follows.  The  body  is  supposed  to  be  composed  of  the  quan- 
tities ?7«j,  //ig,  i^a  '^^  tlie  substances  ^S*,,  /S'g,  S^^  the  value  of  m^  -(" 
mg  +  mg  being  unity.  Let  Pj,  P^,  P3  be  any  three  points  in  the 
plane,  which  are  not  in  the  same  straight  line.  If  we  suppose  masses 
equal  to  m^,  mg,  m^  to  be  placed  at  these  three  points,  the  center  of 
gravity  of  these  masses  will  determine  a  point  which  will  indicate 
the  value  of  these  quantities.  If  the  triangle  is  equiangular  and  has 
the  height  unity,  the  distances  of  the  point  from  the  three  sides  will 
be  equal  numerically  to  «?j,  m,,  m^.  Now  if  for  every  possible 
phase  of  the  components,  of  a  given  temperature  and  pressure,  we 
lav  off  from  the  point  in  the  X-  Y  plane  which  represents  the  compo- 
sition of  the  phase  a  distance  measured  parallel  to  the  axis  of  Z  and 
representing  the  value  of  C  (when  ni^-\-n)2-\-'mQ=.\),  the  points 
thus  determined  will  form  a  surface,  which  may  be  designated  as  the 
mj-mg-^Vg-C  surface  of  the  substances  considered,  or  simply  as  their 
m-t,  surface,  for  the  given  temperature  and  pressure.  In  like  manner, 
when  there  are  but  two  component  substances,  we  may  obtain  a 
curve,  which  we  will  suppose  in  the  X-Z  plane.  The  coordinate  y 
may  then  represent  temperature  or  pressure.  But  we  will  limit  our- 
selves to  the  consideration  of  the  properties  of  the  m-X,  surface  for 
w  =r  3,  or  the  m-l  curve  for  n  =z  2,  regarded  as  a  surface,  or  curve, 
which  varies  with  the  temperature  and  pressure. 

As  by  (96)  and  (92) 

and  (for  constant  temperature  and  pressure) 

d'Q  =  f.1^  dm  J  -f-  yWg  ^^'^2  +  /^3  dm^, 
if  we  imagine  a  tangent  plane  for  the  point  to  which  these  letters 
relate,  and  denote  by  l'  the  ordinate   for   any  point   in   the  plane, 


J.  W.   Gihbs — Equilibrium  oj' Heterogeneous  /Substances.      177 

and  by  >«,',  wig'j  "^a'j  ^^^^  distances  of  the  foot  of  this  ordinate  from 
the  three  sides  of  the  triangle  Pj  P3  Pg,  we  may  easily  obtain 

C'  =  /(,mj'  +  /-/o  Wo'  +  Ms  "'3',  (199) 

which  we  may  regard  as  the  equation  of  the  tangent  plane.  There- 
fore the  ordinates  for  this  plane  at  P^,  P,,  and  P3  are  equal  respect- 
ively to  the  potentials  yu,,  yUg?  'i^^*^  /'s-  -"^nd  in  general,  the  ordinate 
for  any  point  in  the  tangent  plane  is  equal  to  the  potential  (in  the 
phase  represented  by  the  point  of  contact)  for  a  substance  of  which 
the  composition  is  indicated  by  the  position  of  the  ordinate.  (See 
page  149.)  Among  the  bodies  which  may  be  formed  of  S^,  aS^,  and 
-83,  there  may  be  some  which  are  incapable  of  variation  in  composi- 
tion, or  which  are  capable  only  of  a  single  kind  of  variation.  These 
will  be  represented  by  single  points  and  curves  in  vertical  planes. 
Of  the  tangent  plane  to  one  of  these  curves  only  a  single  line  will  be 
fixed,  which  will  determine  a  series  of  potentials  of  which  only  two 
will  be  independent.  The  phase  represented  by  a  separate  point  will 
determine  only  a  single  potential,  viz.,  the  potential  for  the  substance 
of  the  body  itself,  which  will  be  equal  to  'C. 

The  points  representing  a  set  of  coexistent  phases  have  in  general 
a  common  tangent  plane.  But  when  one  of  these  points  is  situated 
on  the  edge  where  a  sheet  of  the  surface  terminates,  it  is  sufficient  if 
the  plane  is  tangent  to  the  edge  and  passes  below  the  surface.  Or, 
when  the  point  is  at  the  end  of  a  separate  line  belonging  to  the  sur- 
face, or  at  an  angle  in  the  edge  of  a  sheet,  it  is  sufficient  if  the  plane 
pass  through  the  point  and  below  the  line  or  sheet.  If  no  part  of  the 
surface  lies  below  the  tangent  plane,  the  points  where  it  meets  the 
plane  will  represent  a  stable  (or  at  least  not  unstable)  set  of  co- 
existent phases. 

The  surface  which  we  have  considered  represents  the  relation 
between  'C,  and  m^,  m^,  m„  for  homogeneous  bodies  when  t  and  jo 
have  any  constant  values  and  ni^  -|-  m^  -f-^s  =  1-  It  will  often  be 
useful  to  consider  the  surface  which  represents  the  relation  between 
the  same  variables  for  bodies  which  consist  of  parts  in  different  but 
coexistent  phases.  We  may  suppose  that  these  are  stable,  at  least  in 
regard  to  adjacent  phases,  as  otherwise  the  case  would  be  devoid  of 
interest.  The  point  which  represents  the  state  of  the  composite 
body  will  evidently  be  at  the  center  of  gravity  of  masses  equal  to 
the  parts  of  the  body  placed  at  the  points  representing  the  phases  of 
these  parts.  Hence  from  the  surface  representing  the  properties  of 
homogeneous  bodies,  which  may  be  called  the  primitive  surface,  we 

Trans.  Conn.  Acad.,  Vol.  III.  23  January,  1876. 


178      tT.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 

may  easily  construct  the  surface  representing  the  properties  of  bodies 
which  ai-e  in  equilibrium  but  not  homogeneous.  This  may  be  called 
the  secondary  or  derived  surface.  It  will  consist,  in  general,  of 
various  portions  or  sheets.  The  sheets  which  represent  a  combina- 
tion of  two  phases  may  be  formed  by  rolling  a  double  tangent  plane 
upon  the  primitive  surface :  the  part  of  the  envelop  of  its  successive 
positions  which  lies  between  the  curves  traced  by  the  points  of  con- 
tact will  belong  to  the  derived  surface.  When  the  primitive  surface 
has  a  triple  tangent  plane  or  one  of  higher  order,  the  triangle  in  the 
tangent  plane  formed  by  joining  the  points  of  contact,  or  the  smallest 
polygon  without  re-entrant  angles  which  includes  all  the  points  of 
contact,  will  belong  to  the  derived  surface,  and  will  represent  masses 
consisting  in  general  of  three  or  more  phases. 

Of  the  whole  thermodynamic  surface  as  thus  constructed  for  any 
temperature  and  any  positive  pressure,  that  part  is  especially  impor- 
tant which  gives  the  least  value  of  !:  for  any  given  values  of  Wj,  ?«2? 
m^.  The  state  of  a  mass  represented  by  a  point  in  this  part  of  the 
surface  is  one  in  which  no  dissipation  of  energy  would  be  possible  if 
the  mass  were  enclosed  in  a  i-igid  envelop  impermeable  both  to 
matter  and  to  heat ;  and  the  state  of  any  mass  composed  of  aS^,  aSj,  S^ 
in  any  proportions,  in  which  the  dissipation  of  energy  has  been  com- 
pleted, so  far  as  internal  processes  are  concerned,  (i.  e.,  under  the 
limitations  imposed  by  such  an  envelop  as  above  supposed,)  would  be 
represented  by  a  point  in  the  part  which  we  are  considering  of  the 
in-'Q  surface  for  the  temperature  and  pressure  of  the  mass.  We  may 
therefore  briefly  distinguish  this  part  of  the  surface  as  the  surface  of 
dissipated  energy.  It  is  evident  that  it  forms  a  continuous  sheet,  the 
projection  of  which  upon  the  X-  Y  plane  coincides  with  the  triangle 
Pj  P2  P3,  (except  when  the  pressure  for  which  the  m-?  surface  is 
constructed  is  negative,  in  which  case  there  is  no  surface  of  dissipated 
energy,)  that  it  nowhere  has  any  convexity  upward,  and  that  the 
states  which  it  represents  are  in  no  case  unstable. 

The  general  properties  of  the  m-t,  lines  for  two  component  sub- 
stances are  so  similar  as  not  to  require  separate  consideration.  We 
now  proceed  to  illustrate  the  use  of  both  the  surfaces  and  the  lines 
by  the  discussion  of  several  particular  cases. 

Three  coexistent  phases  of  two  component  substances  may  be 
represented  by  the  points  A,  B,  and  C,  in  figure  ],  in  which  I  is 
measured  toward  the  top  of  the  page  from  PjPg,  '" ,  toward  the  left 
from  P2Q2,  and  m^  toward  the  right  from  P,Qi.  It  is  supposed 
that  P1P2  =  1-     Portions  of  the  curves  to  which  these  points  belong 


J.  W.  Gibhs — .Equilihriiim  of  Heterogeneous  Sithstances.       179 


are  seen  in  the  figure,  and  will  be  denoted  by  the  symbols  (A),  (B), 
(C).  We  may,  for  convenience,  speak  of  these  as  separate  curves, 
without  implying  anything  in  regard  to  their  possible  continuity  in 
parts  of  the  diagram  remote  from  their  common  tangent  AC.  The 
line  of  dissipated  energy  includes  the  straight  line  AC  and  portions 
of  the  primitive  curves  (A)  and  (C).     Let  us  first  consider  how  the 

diagram  will  be  altered,  if  the  temper- 
ature is  varied  while  the  pressure  re- 
mains constant.  If  the  temperature 
receives  the  increment  dt,  an  ordinate 
of  which  the  position  is  fixed  will 
'd'Q^ 


Q. 


b 
Fig.  1. 


P. 


receive  the  increment  (  -^  1         dt,    or 

\dt I p^  m 

—  //  dt.  (The  reader  will  easily  con- 
vince himself  that  this  is  true  of  the 
ordinates.  for  the  secondary  line  AC,  as  well  as  of  the  ordinates  for 
the  primitive  curves.)  Now  if  we  denote  by  ;/'  the  entropy  of  the 
phase  represented  by  the  point  B  considered  as  belonging  to  the 
curve  (B),  and  by  rf  the  entropy  of  the  composite  state  of  the  same 
matter  represented  by  the  point  B  considered  as  belonging  to  the 
tangent  to  the  curves  (A)  and  (C),  t  (?/'  —  //')  will  denote  the  heat 
yielded  by  a  unit  of  matter  in  passing  from  the  first  to  the  second 
of  these  states.  If  this  quantity  is  positive,  an  elevation  of  temper- 
ature will  evidently  cause  a  part  of  the  curve  (B)  to  protrude  below 
the  tangent  to  (A)  and  (C),  which  will  no  longer  form  a  part  of  the 
line  of  dissipated  energy.  This  line  will  then  include  portions  of  the 
three  curves  (A),  (B),  and  (C),  and  of  the  tangents  to  (A)  and  (B) 
and  to  (B)  and  (C).  On  the  other  hand,  a  lowering  of  the  tempera- 
ture will  cause  the  curve  (B)  to  lie  entirely  above  the  tangent  to  (A) 
and  (C),  so  that  all  the  phases  of  the  sort  represented  by  (B)  will  be 
unstable.  If  t  {i/  —  ;/")  is  negative,  these  efl:ects  will  be  produced  by 
the  opposite  changes  of  temperature. 

The  effect  of  a  change  of  pressure  while  the  temperature  remains 
constant  may  be  found  in  a  manner  entirely  analogous.     The  varia- 


dp  or  V  dp.      Therefore,  if   the 


tion  of  any  ordinate  will  be  (  ^ 

^  \dplt,;,i 

volume  of  the  homogeneous  phase  represented  by  the  point  B  is 
a  greater  than  the  volume  of  the  same  matter  divided  betAveen  the 
the  phases  represented  by  A  and  C,  an  increase  of  pressure  will  give 
diagi'am  indicating  that  all  phases  of  the  sort  represented  by  curve 
(B)  are  unstable,  and  a  decrease  of  pressure  will  give  a  diagram  indi- 


180      J.  W.  Gibbs — Equilibruim  of  Heterogeneous  Substances. 


eating  two  stable  pairs  of  coexistent  phases,  in  each  of  which  one  of 
the  pliases  is  of  the  sort  represented  by  the  curve  (B).  When  the 
relation  of  the  volumes  is  the  reverse  of  that  supposed,  these  results 
will  be  produced  by  the  opposite  changes  of  pressure. 

When  we  have  four  coexistent  phases  of  three  component  substances, 
there  are  two  cases  which  must  be  distinguished.  In  the  iirst,  one  of 
the  points  of  contact  of  the  primitive  surface  with  the  qiaadruple 
tangent  plane  lies  within  the  triangle  formed  by  joining  the  other 
three  ;  in  the  second,  the  four  points  may  be  joined  so  as  to  form  a 
quadrilateral  without  re-entrant  angles.  Figure  2  repi-esents  the 
projection  upon  the  A'^  Y  plane  (in  which  ni^,  m^,  m^  are  measured) 
of  a  part  of  the  snrftice  of  dissipated  energy,  when  one  of  the  points 
of  contact  D  falls  within  the  triangle  formed  by  the  other  thi-ee  A,  B, 
0.  This  surface  includes  the  triangle  ABC  in  the  quadruple  tangent 
plane,  portions  of  the  three  sheets  of  the  primitive  surface  which 
touch  the  triangle  at  its  vertices,  EAF,  GBH,  ICK,  and  portions  of 
the  three  developable  surfaces  formed  by  a  tangent  plane  rolling 
upon  each  pair  of  these  sheets.     These  developable  surfaces  are  repre- 


FlG.   2. 

sented  in  the  figure  by  ruled  surfaces,  the  lines  indicating  the  direc- 
tion of  their  rectilinear  elements.  A  point  within  the  triangle  ABC 
represents  a  mass  of  which  the  matter  is  divided,  in  general,  between 
three  or  four  different  phases,  in  a  manner  not  entirely  determined  by 
the  position  of  a  point.  (The  quantities  of  matter  in  these  phases  are 
such  that  if  placed  at  the  cori-esponding  points.  A,  B,  C,  D,  their 
center  of  gravity  would  be  at  the  point  representing  the  total  mass.) 


J.  W.  Gihbs — Equilibrium  of  Heterogeneous  Substances.     181 

Such  a  mass,  if  exposed  to  constant  temperature  and  pressure,  would 
be  in  neutral  equilibrium.  A  point  in  the  developable  surfaces  repre- 
sents a  mass  of  which  the  matter  is  divided  between  two  coexisting 
phases,  which  are  represented  by  the  extremities  of  the  line  iu  the 
figure  passing  through  that  point.  A  point  in  the  primitive  surface 
rejjresents  of  course  a  homogeneous  mass. 

To  determine  the  eftect  of  a  change  of  temperature  without  change 
of  pressure  upon  the  general  features  of  the  surface  of  dissipated 
energy,  we  must  know  whether  heat  is  absorbed  or  yielded  by  a 
mass  in  passing  from  the  phase  represented  by  the  point  D  in  the 
primitive  surface  to  the  composite  state  consisting  of  the  phases  A, 

B,  and  C  which  is  represented  by  the  same  point.  If  the  first  is  the 
case,  an  increase  of  temperature  will  cause  the  sheet  (D)  (i.  e.,  the 
sheet  of  the  primitive  surface  to  which  the  point  D  belongs)  to  sep- 
ai-ate  from  the  plane  tangent  to  the  three  other  sheets,  so  as  to  be 
situated  entirely  above  it,  and  a  decrease  of  temperature,  will  cause 
a  part  of  the  sheet  (D)  to  protrude  through  the  plane  tangent  to 
the  other  sheets.  These  effects  will  be  produced  by  the  opposite 
changes  of  temperature,  when  heat  is  yielded  by  a  mass  passing 
from  the  homogeneous  to  the  composite  state  above  mentioned. 

In  like  manner,  to  determine  the  effect  of  a  vai-iation  of  pressure 
without  change  of  temperature,  we  must  know  whether  the  volume 
for  the  homogeneous  phase  represented  by  D  is  greater  or  less  than 
the  volume  of  the  same  matter  divided  between  the  phases  A,  B,  and 

C.  If  the  homogeneous  phase  has  the  greater  volume,  an  increase  of 
pressure  will  cause  the  sheet  (D)  to  separate  from  the  plane  tangent  to 
the  other  sheets,  and  a  diminution  of  pressure  will  cause  a  pai't  of  the 
sheet  (D)  to  protrude  below  that  tangent  plane.  And  these  effects 
will  be  produced  by  the  opposite  changes  of  pressure,  if  the  homoge- 
neous phase  has  the  less  volume.  All  this  appears  from  precisely  the 
same  considerations  which  were  used  in  the  analogous  case  for  two 
component  substances. 

Now  when  the  sheet  (D)  rises  above  the  plane  tangent  to  the  other 
sheets,  the  general  features  of  the  surface  of  dissipated  energy  are 
not  altered,  except  by  the  disappearance  of  the  point  D.  But  when 
the  sheet  (D)  protrudes  below  the  plane  tangent  to  the  other  sheets, 
the  surface  of  dissipated  energy  will  take  the  form  indicated  in  figure  3. 
It  will  include  portions  of  the  four  sheets  of  the  primitive  sui-face, 
portions  of  the  six  developable  surfaces  formed  by  a  double  tangent 
plane  rollino-  upon  these  sheets  taken  two  by  two,  and  portions  of 
three  triple  tangent  planes  for  these  sheets  taken  by  threes,  the  sheet 
(D)  being  always  one  of  the  three. 


182      -T.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 


But  when  the  points  of  contact  with  the  quadruple  tangent  plane 
which  represent  the  four  coexistent  phases  can  be  joined  so  as  to 
form  a  quadrilateral  ABCD  (fig.  4)  without  reentrant  angles,  the 
surface  of  dissipated  energy  will  include  this  plane  quadrilateral, 
portions  of  the  four  sheets  of  the  primitive  surface  which  are  tangent 
to  it,  and  portions  of  the  four  developable  surfaces  formed  by  double 


Fig.  4. 


Fig.  5. 


tangent  planes  rolling  upon  the  four  pairs  of  these  sheets  which  corres- 
pond to  the  four  sides  of  the  quadrilateral.  To  determine  the  gen- 
eral eifect  of  a  variation  of  temperature  upon  the  surface  of  dissipated 
energy,  let  us  consider  the  composite  states  represented  by  the  point 
I  at  the  intersection  of  the  diagonals  of  the  quadrilateral.  Among 
these  states  (which  all  relate  to  the  same  kind  and  quantity  of  matter) 
there  is  one  which  is  composed  of  the  phases  A  and  C,  and  another 
which  is  composed  of  the  phases  B  and  D.  Now  if  the  entropy  of 
the  first  of  these  states  is  greater  than  that  of  the  second,  (i.  e.,  if 
heat  is  given  ovit  by  a  body  in  passing  from  the  first  to  the  second 
state  at  constant  temperature  and  pi'essure,)  which  we  may  suppose 
without  loss  of  generality,  an  elevation  of  temperature  while  the 
pi'essure  remains  constant  will  cause  the  triple  tangent  planes  to 
(B),  (D),  and  (A),  and  to  (B),  (D),  and  (C),  to  rise  above  the 
triple  tangent  planes  to  (A),  (C),  and  (B),  and  to  (A),  (C), 
and  (D),  in  the  vicinity  of  the  point  I.  The  surface  of  dissipated 
energy  will  therefore  take  the  form  indicated  in  figure  5,  in  which 
there  are  two  plane  triangles  and  five  developable  surfaces  besides 
portions  of  the  four  primitive  sheets.  A  diminution  of  temperature 
wall  give  a  different  but  entirely  analogous  form  to  the  surface  of  dis- 
sipated energy.  The  quadrilateral  ABCD  will  in  this  case  break 
into  two  triangles  along  the  diameter  BD.     The  effects  produced  by 


J.  TF.  Gibhs — Equilibrmm  of  Heterogeneoxis  Substances.      183 

variation  of  the  pressure  wliile  the  temperature  remains  constant  will 
of  course  be  similar  to  those  described.  By  considering  the  diiference 
of  volume  instead  of  the  difference  of  entropy  of  the  two  states  repi-e- 
sented  by  the  point  I  in  the  quadruple  tangent  plane,  we  may  distin- 
guish between  the  effects  of  increase  and  diminution  of  pressure. 

It  should  be  observed  that  the  points  of  contact  of  the  quadruple 
tangent  plane  with  the  primitive  surface  may  be  at  isolated  points  or 
curves  belonging  to  the  latter.  So  also,  in  the  case  of  two  component 
substances,  the  points  of  contact  of  the  triple  tangent  line  may  be  at 
isolated  points  belonging  to  the  primitive  curve.  Such  cases  need 
not  be  separately  treated,  as  the  necessary  modifications  in  the  pre- 
ceding statements,  when  applied  to  such  cases,  are  quite  evident. 
And  in  the  remaining  discussion  of  this  geometrical  method,  it  will 
generally  be  left  to  the  reader  to  make  the  necessary  limitations  or 
modificatioiis  in  analogoiis  cases. 

The  necessary  condition  in  regard  to  simultaneous  variations  of 
temperature  and  pressure,  in  order  that  four  coexistent  phases  of 
three  components,  or  three  coexistent  phases  of  two  components,  shall 
remain  possible,  has  already  been  deduced  by  purely  analytical  pro- 
cesses.    (See  equation  (129).) 

We  will  next  consider  the  case  of  two  coexistent  phases  of  identi- 
cal composition,  and  first,  when  the  number  of  components  is  two. 
The  coexistent  phases,  if  each  is  variable  in  composition,  will  be 
represented  by  the  point  of  contact  of  two  curves.  One  of  the 
curves  will  in  general  lie  above  the  other  except  at  the  point  of  con- 
tact ;  therefore,  when  the  temperature  and  pressure  remain  constant, 
one  phase  cannot  be  varied  in  composition  without  becoming  unstable, 
while  the  other  phase  will  be  stable  if  the  proportion  of  either  com- 
ponent is  increased.  By  varying  the  temperature  or  pressure,  we 
may  cause  the  upper  curve  to  protrude  below  the  other,  or  to  rise 
(relatively)  entirely  above  it.  (By  comparing  the  volumes  or  the 
entropies  of  the  two  coexistent  phases,  we  may  easily  determine 
which  result  would  be  produced  by  an  increase  of  temperature  or 
of  pressure.)  Hence,  the  temperatures  and  pressures  for  which  two 
coexistent  phases  have  the  same  composition  form  the  limit  to  the 
temperatures  and  pressures  for  which  such  coexistent  phases  are  pos- 
sible. It  will  be  observed  that  as  we  pass  this  limit  of  temperature 
and  pressure,  the  pair  of  coexistent  phases  does  not  simply  become 
unstable,  like  pairs  and  triads  of  coexistent  phases  which  we  have 
considered  before,  but  there  ceases  to  be  any  such  pair  of  coexistent 
phases.     The  same  result  has  already  been  obtained  analytically  on 


184      J.  W.  Gibbs — Equilibrmm  of  Heterogeneous  Substances. 

page  155.     But  on  that  side  of  the  limit  on  which  the  coexistent 
phases  are  possible,  there  will  be  two  pairs  of  coexistent  phases  for 
the  samj  values  of  t  and  />,  as  seen  in  figure  6.    If  the  curve  AA'  repre- 
sents vapor,  and  the  curve  BB'  liquid,  a  liquid 
(represented  by)  B  may  exist  in  contact  with 
a  vapor  A,  and  (at  the  same  temperature  and 
pressure)  a  liquid  B'  in  contact  with  a  vapor 
A',     If  we  compare  these  phases  in  respect  to 
their  composition,  we  see  that  in  one  case  the 
^^'  ^'  vapor  is  richer  than  the  liquid  in  a  certain 

component,  and  in  the  other  case  poorer.  Therefore,  if  these  liquids 
are  made  to  boil,  the  effect  on  their  composition  will  be  opposite.  If 
the  boiling  is  continued  under  constant  pressure,  the  temperature  will 
rise  as  the  liquids  approach  each  other  in  composition,  and  the  curve 
BB'  will  rise  relatively  to  the  curve  AA',  until  the  curves  are  tangent 
to  each  other,  when  the  two  liquids  become  identical  in  nature,  as  also 
the  vapors  which  they  yield.  In  composition,  and  in  the  value  of  'Q  per 
unit  of  mass,  the  vapor  will  then  agree  with  the  liquid.  But  if  the 
curve  BB'  (which  has  the  greater  curvature)  represents  vapor,  and 
AA'  represents  liquid,  the  effect  of  boiling  will  make  the  liquids  A 
and  A'  differ  more  in  composition.  In  this  case,  the  relations  indi- 
cated in  the  figure  will  hold  for  a  temperature  higher  than  that  for 
which  (with  tlie  same  pressure)  the  curves  are  tangent  to  one  another. 
When  two  coexistent  phases  of  three  component  substances  have 
the  same  composition,  they  are  represented  by  the  point  of  contact  of 
two  sheets  of  the  primitive  surface.  If  these  sheets  do  not  intersect 
at  the  point  of  contact,  the  case  is  very  similar  to  that  which  we  have 
just  considered.  The  upper  sheet  except  at  the  point  of  contact 
represents  unstable  phases.  If  the  temperature  or  pressure  are  so 
varied  that  a  part  of  the  upper  sheet  protrudes  through  the  lower,  the 
points  of  contact  of  a  double  tangent  plane  rolling  upon  the  two 
sheets  will  describe  a  closed  curve  on  each,  and  the  surface  of  dissi- 
pated energy  will  include  a  portion  of  each  sheet  of  the  primitive  sur- 
face united  by  a  ring-shaped  developable  surface. 

If  the  sheet  having  the  greater  curvatures  represents  liquid,  and 
the  other  sheet  vapor,  the  boiling  temperature  for  any  given  pressure 
will  be  a  maximum,  and  the  pressure  of  saturated  vapor  for  any  given 
temperature  will  be  a  minimun,  when  the  coexistent  liquid  and  vapor 
have  the  same  composition. 

But  if  the  two  sheets,  constructed  for  the  temperature  and  pressure 
of  the  coexistent  phases  which  have  the  same  composition,  intersect 


./  W.  Gihbs — Equilibrium,  of  Ileterogeneoiis  Substances.      185 

at  the  point  of  contact,  the  wliole  primitive  surface  as  seen  from 
below  will  in  general  present  four  re-entrant  furrows,  radiating  from 
the  point  of  contact,  for  each  of  which  a  developable  surface  may  he 
formed  by  a  rolling  double  tangent  plane.  The  diiferent  parts  of  the 
surface  of  dissipated  energy  in  the  vicinity  of  the  })oint  of  contact  are 
represented  in  figure  7.  ATB,  ETF  are  parts  of  one  sheet  ot  the 
primitive  surface,  and  CTD,  GTH  are  parts  of  the  other.  These  are 
united  by  the  developable  surfaces  BTC,  DTE,  FTG,  HTA.  Now 
we  may  make  either  sheet  of  the  primitive  surface  sink  relatively  to 
the  other  by  the  pi'oper  variation  of  temperature  or  pressure.  If  the 
sheet  to  which  ATB,  ETF  belong  is  that  which  sinks  relatively,  these 

parts  of  the  surface  of  dissipated  energy  will 

be  merged  in  one,  as  well  as  the  developable 

surfaces  BTC,  DTE,  and  also  FTG,  HTA. 

.(The   lines   CTD,    BTE,   ATE,   HTG    will 

separate  from  one  another  at  T,  each  forming 

a  continuous  curve.)     But  if  the  sheet  of  the 

primitive  surface   which   sinks  relatively  is 

that  to  which  CTD  and  GTH  belong,  then 

Fig.  7.  these  parts  will  be  merged  in  one  in  the  sur- 

fiice  of  dissipated  energy,  as  will  be  the  developable  surfaces  BTC, 

ATH,  and  also  DTE,  FTG. 

It  is  evident  that  this  is  not  a  case  of  maximum  or  minimum  tem- 
perature for  coexistent  phases  under  constant  pressure,  or  of  maximum 
or  minimum  pressure  for  coexistent  phases  at  constant  temperature. 

Another  case  of  intei*est  is  when  the  composition  of  one  of  three 
coexistent  phases  is  such  as  can  be  produced  by  combining  the  other 
two.  In  this  case,  the  primitive  surface  must  touch  the  same  plane 
in  three  points  in  the  same  straight  line.  Let  us  distinguish  the  parts 
of  the  primitive  surface  to  which  these  points  belong  as  the  sheets  (A), 
(B),  and  (C),  (C)  denoting  that  which  is  intermediate  in  position. 
The  sheet  (C)  is  evidently  tangent  to  the  developable  surface  formed 
upon  (A)  and  (B).  It  may  or  it  may  not  intersect  it  at  the  point  of 
contact.  If  it  does  not,  it  must  lie  above  the  developable  sur- 
face, (unless  it  represents  states  which  are  unstable  in  regard 
to  continuous  changes,)  and  the  surface  of  dissipated  energy 
will  include  parts  of  the  primitive  sheets  (A)  and  (B),  the  develop- 
able surface  joining  them,  and  the  single  point  of  the  sheet  (C) 
in  which  it  meets  this  developable  surface.  Now,  if  the  tempera- 
ture or  pressure  is  varied  so  as  to  make  the  sheet  (C)  rise  above  the 
Tkans.  Conn.  Acad.,  Vol.  III.  24  February,  1876. 


1 86      ./  W.  Gibhs—Equilibrluni  of  Heterogeneous  Stihstances. 


(levelopable  surface  formed  on  the  sheets  (A)  and  (B),  the  surface  of 
dissipated  energy  will  be  altered  in  its  general  features  only  by  the 
removal  of  the  single  point  of  the  sheet  (C).  But  if  the  temperature 
or  pressure  is  altei-ed  so  as  to  make  a  part  of  the  sheet  (C)  protrude 
through  the  developable  surface  formed  on  (A)  and  (B),  the  surface 

b  of  dissipated  energy  will  have  the 
form  indicated  in  figure  8.  It 
will  include  two  plane  triangles 
ABC  and  A'B'C,  a  part  of  each  of 
the  sheets  (A)  and  (B),  represented 
in  the  figure  by  the  spaces  on  the 
left  of  the  line  aAiV'a'  and  on  the 
\  right  of  the  line  bBB'b',  a  small 
^i«-  8-  "  part  CC  of  the  sheet  (C),  and  de- 

velopable surfaces  formed  upon  these  sheets  taken  by  pairs  ACC'A', 
BCC'B',  aABb,  a'A'B'b'.  the  last  two  being  dilFerent  portions  of  the 
same  developable  surface. 

But  if,  when  the  primitive  surface  is  constructed  for  such  a 
temperature  and  pressui-e  that  it  has  three  points  of  contact  with 
the  same  plane  in  the  same  straight  line,  the  sheet  (C)  (which  has 
the  middle  position)  at  its  point  of  contact  with  the  triple  tangent 
plane  intersects  the  developable  surface  formed  upon  the  other  sheets 
(A)  and  (B),  the  surface  of  dissipated  energy  will  not  include  this 
developable  surface,  but  will  consist  of  portions  of  the  three  primi- 
tive sheets  with  two  developable  surfaces  formed  on  (A)  and  (C)  and 
on  (B)  and  (C).  These  developable  surfaces  meet  one  another  at 
the  point  of  contact  of  (C)  with  the  triple  tangent  plane,  dividing  the 

portion  of  this  sheet  which  be- 
c      7  longs  to  the  surface  of  dissipated 

energy  into  two  parts.  If  now 
the  temperature  or  pressure  are 
varied  so  as  to  make  the  sheet 
((3)  sink  relatively  to  the  de- 
velopable surface  formed  on  (A) 
b'  and  (B),  the  only  alteration  in 
the  general  features  of  the  sur- 
face of  dissipated  energy  will 
be  that  the  developable  surfaces 
formed  on  (A)  and  (C)  and  on  (B)  and  (C)  will  separate  from 
one  another,  and  the  two  parts  of  the  sheet  (C)  will  be  merged  in 
one.     But  a  contrary  variation  of  temperature  or  pressure  will  give  a 


./.  W.  Gihbs — Eqailibrlum  of  Hetet'oyeneoufi  /Substances.       187 

surface  of  dissipated  energy  such  as  is  represented  in  figure  (9),  con- 
taining two  plane  triangles  ABC,  A'B'C  belonging  to  triple  tangent 
planes,  a  portion  of  the  sheet  (A)  on  the  left  of  the  line  aA A'a',  a  por- 
tion of  the  sheet  (B)  on  the  right  of  the  line  bBB'b',  two  separate 
portions  cCy  and  c'C'y'  of  the  sheet  (C),  two  separate  portions  aACc 
and  a'A'C'c'  of  the  developable  surface  formed  on  (A)  and  (C),  two 
separate  portions  bBC;/  and  h'B'C'y'  of  the  developable  surface 
formed  on  (B)  and  (C),  and  the  portion  A'ABB'  of  the  developable 
surface  formed  on  (A)  and  (B). 

From  these  geometrical  relations  it  appears  that  (in  general)  the 
temperature  of  three  coexistent  phases  is  a  maximum  or  minimum  for 
constant  pressure,  and  the  pressure  of  three  coexistent  phases  a  maxi- 
mum or  mininuim  for  constant  temperature,  when  the  composition  of 
the  three  coexistent  phases  is  such  that  one  can  be  formed  by  com- 
bining the  other  two.  This  result  has  been  obtained  analytically 
on  page  156. 

The  preceding  examples  are  amply  sufficient  to  illustrate  the  use 
of  the  m-'C,  surfaces  and  curves.  The  physical  properties  indicated  by 
the  nature  of  the  siirface  of  dissipated  energy  have  been  only  occa- 
sionally mentioned,  as  they  are  often  far  more  distinctly  indicated  by 
the  diagrams  than  they  could  be  in  words.  It  will  be  observed  that 
a  knowledge  of  the  lines  which  divide  the  various  different  portions 
of  the  surface  of  dissipated  energy  and  of  the  direction  of  the  recti- 
linear elements  of  the  developable  surfaces,  as  projected  upon  the 
JC-Y'  plane,  without  a  knowledge  of  the  form  of  the  m-'Q  surface  in 
space,  is  sufficient  for  the  determination  (in  respect  to  the  quantity 
and  composition  of  the  resulting  masses)  of  the  combinations  and 
separations  of  the  substances,  and  of  the  changes  in  their  states  of 
aggregation,  which  take  place  when  the  substances  are  exposed  to 
the  temperature  and  pressure  to  which  the  projected  lines  relate, 
except  so  far  as  such  transformations  are  prevented  by  passive  re- 
sistances to  change. 

CRITICAL    PHASES. 

It  has  been  ascertained  by  experiment  that  the  variations  of  two 
•coexistent  states  of  the  same  substance  are  in  some  cases  limited  in 
one  direction  by  a  terminal  state  at  which  the  distinction  of  the 
coexistent  states  vanishes.*  This  state  has  been  called  the  critical 
state.  Analogous  properties  may  doubtless  be  exhibited  by  com- 
pounds of  variable  composition  without  change  of  tempei-ature  or 

*  See  Dr.  Andrews  "  On  the  continuity  of  the  gaseous  and  liquid  states  of  matter." 
Phil.  Trans.,  vol.  159,  p.  575. 


I  88      J.    IK  Gibbs — Equ'dibruuii.  of  Heterogeneous  Substances. 

pivssuro.  For  if,  ;it  iiiiy  given  tcniixTutuiv  and  pressure,  two  liquids 
nre  ca})iil)le  of  forming  a  stable  mixture  in  any  ratio  in  ^  :  m^  less  than 
rt,  and  in  any  greater  than  A,  n  and  h  being  the  values  of  that  ratio 
for  two  coexistent  ))hases,  while  either  can  form  a  stable  mixture  with 
a  third  licjuid  in  all  jtroportions,  and  any  small  quantities  of  the  iirst 
and  second  can  unite  at  once  with  a  great  quantity  of  the  third  to 
form  a  stable  mixture,  it  may  easily  be  seen  that  two  coexistent  mix- 
tures of  the  three  liquids  may  be  varied  in  composition,  the  tempera- 
ture and  pressure  remaining  the  same,  from  initial  phases  in  each  of 
which  the  (piantity  of  the  third  liquid  is  nothing,  to  a  terminal  phase 
in  whicli  the  distinction  of  the  two  phases  vanishes. 

In  general,  we  may  define  a  critical  phase  as  one  at  which  the  dis- 
tinction between  coexistent  i>hases  vanishes.  We  may  suppose  the 
coexistent  phases  to  be  stable  in  respect  to  continuous  changes,  for 
although  I'elations  in  some  icspects  analogous  might  be  imagined  to 
hold  true  in  regard  to  ])hases  which  are  unstable  in  respect  to  con- 
tinuous changes,  the  discussion  of  siudi  cases  would  be  devoid  of 
interest.  But  if  the  coexistent  jthases  and  the  critical  phase  are 
unstable  only  in  respect  to  the  possible  formation  of  phases  entirely 
ditferent  from  the  critical  and  adjacent  phases,  the  liability  to  such 
changes  will  in  no  respect  affect  the  relations  between  the  critical  and 
adjacent  jdiases,  and  need  not  be  considered  in  a  theoretical  discussion 
of  these  relations,  although  it  may  prevent  an  experimental  realiza- 
tion of  the  phases  considered.  For  the  sake  of  brevity,  in  the  follow- 
ing discussion,  ])hases  in  tlu^  vicinity  of  the  critical  phase  will  gen- 
erally be  called  stable,  if  they  are  unstable  only  in  respect  to  the 
formation  of  phases  entirely  different  from  any  in  the  vicinity  of  the 
critical  phase. 

Let  us  first  consider  the  number  of  independent  variations  of  which 
a  critical  phase  (while  remaining  such)  is  capable.  If  we  denote  by 
n  the  number  of  indejiendently  variable  components,  a  pair  of  coexis- 
tent phases  will  be  capable  of  n  independent  variations,  which  may  be 
expressed  by  the  variations  of  ti  of  the  quantities  t,  p,  //^,  //^,  ...//„. 
If  we  limit  these  variations  by  giving  to  n  —  1  of  the  quantities  the 
constant  values  which  they  have  for  a  certain  critical  phase,  we 
obtain  a  linear*  series  of  pairs  of  coexistent  phases  terminated  by  the 
critical  phase.  If  we  now  vary  infinitesimally  the  values  of  these 
n  —  l  quantities,  we  shall  have  for  the  new  set  of  values  considered  con- 
stant a  new  linear  series  of  pairs  of  coexistent  phases.  Now  for  every 
pair  of  phases  in  the  first  series,  there  must  be  pairs  of  phases  in  the 

*  This  tonn  is  used  to  cliaracterize  a  series  having  a  single  degree  of  extension. 


./.  W.  Gtbbs-~Equilibriurn  of  Jleterogeneous  ISubstancts.       189 

second  series  differing  infinitely  little  from  the  pair  in  the  first,  and 
vice  versa^  therefore  the  second  series  of  coexistent  phases  must  be 
terminated  by  a  critical  phase  wliic^h  differs,  but  differs  infinitely 
little,  from  the  first.  We  see,  therefore,  that  if  we  vary  arbitrarily 
the  values  of  any  n  —  1  of  the  quantities  <,^>»,  /^  j,  /^g?  •  •  •  Hn-,  ii«  deter- 
mined by  a  critical  phase,  we  obtain  one  and  only  one  critical  phase 
for  each  set  of  varied  values  ;  i.  c.,  a  critical  phase  is  capable  of 
w— 1  independent  variations. 

The  quantities  t,]>,  //j,  //g,  •  •  .  /^„,  have  the  same  values  in  two 
coexistent  phases,  but  the  ratios  of  the  quantities  ^/,  w,  m,,  rti,^^.  .  .  m„, 
are  in  general  different  in  the  two  j)hases.  Or,  if  for  convenience  we 
compare  equal  volumes  of  the  two  phases  (which  involves  no  loss  of 
generality),  the  quantities  //,  mj,  mg,  ,  ,  .  m„  will  in  general  have 
different  values  in  two  coexistent  phases.  Aj)plying  this  to  coexis- 
tent phases  indefinitely  near  to  a  critical  phase,  we  see  that  in  the 
immediate  vicinity  of  a  critical  phase,  if  the  values  of  n  of  the  quanti- 
ties t,  J),  /u^,  //g?  •  •  •  Mn,  iii'ti  regarded  as  constant  (as  well  as  v),  the 
variations  of  either  of  the  others  will  be  infinitely  small  compared 
with  the  variations  of  the  quantities  ?;,  m^,  rn^,  .  .  .  m„.  This  con- 
dition, which  we  may  write  in  the  form 

(-1^)  =0,  (200) 

characterizes,  as  we  have  seen  on  page  171,  the  limits  which  divide 
stable  from  unstable  phases  in  respect  to  continuous  changes. 

In  fact,  if  we  give  to  the  quantities  t,  /j^,  yUg,  .  .  .  yw„_i  constant 

values  determined  by  a  i)air  of  coexistent  phases,  and  to     *  a  series 

of  values  increasing  from  the  less  to  the  greater  of  the  values  which  it 
has  in  these  coexistent  phases,  we  determine  a  linear  series  of  phases 
connecting  the  coexistent  phases,  in  some  part  of  which  yu„ — since  it 
has  the  same  value  in  the  two  coexistent  phases,  but  not  a  uniform 
value  throughout  the  series  (for  if  it  had,  which  is  theoretically  im- 
probable, all  these  phases  would  be  coexistent) — must  be  a  decreasing 

function  of      ",  or  of  m„,  if  v  also  is  sujjposed  constant.     Therefore, 

the  series  must  contain  phases  which  are  unstable  in  respect  to  con- 
tinuous changes.  (See  page  168.)  And  as  such  a  pair  of  coexistent 
phases  may  be  taken  indefinitely  near  to  any  critical  phase,  the 
unstable  jdiases  (with  resi)ect  to  continuous  changes)  must  approach 
indefinitely  near  to  this  phase. 


190      J.    W.  Gibbs — Equilibrmin  of  Heterogeneous  Substances. 

Critical  phases  have  similar  pi'operties  with  reference  to  stability 
as  determined  with  regard  to  discontinuous  changes.  For  as  every 
stable  phase  which  has  a  coexistent  phase  lies  upon  the  limit  which 
separates  stable  from  unstable  phases,  the  same  must  be  true  of  any 
stable  critical  phase.  (The  same  may  be  said  of  critical  phases  which 
are  unstable  in  regard  to  discontinuous  changes  if  we  leave  out  of 
account  the  liability  to  the  particular  kind  of  discontinuous  change 
in  respect  to  which  the  critical  phase  is  unstable.) 

The  linear  series  of  phases  determined  by  giving  to  n  of  the  quanti- 
ties t,p,Mi-'M2i  '  •  •  /'"  ^^^  constant  values  which  they  have  in  any 
pair  of  coexistent  phases  consists  of  unstable  phases  in  the  part 
between  the  coexistent  phases,  but  in  the  part  beyond  these  phases  in 
eithei"  direction  it  consists  of  stable  phases.  Hence,  if  a  critical  phase 
is  varied  in  such  a  manner  ihntn  of  the  quantities  t,p,  /.i^,  yUg,  .  .  .  /v„ 
remain  constant,  it  will  remain  stable  in  respect  both  to  continuous  and 
to  discontinuous  changes.  Therefore,  yu„.is  an  increasing  function  of 
m„  when  t,  v,  j^i^,  /.I2,  •  •  •  /'n-i  have  constant  values  determined  by 
any  critical  phase.  But  as  equation  (200)  holds  true  at  the  critical 
phase,  the  following  conditions  must  also  hold  true  at  that  phase : 

fd^/n„\ 

=  0,  (201) 


\d}n„^)t,  V, 


^0.  (202) 


If  the  sign  of  equality  holds  in  the  last  condition,  additional  condi- 
tions, concerning  the  differential  coefficients  of  higher  orders,  must  be 
satisfied. 

Equations  (200)  and  (201)  may  in  general  be  called  the  equations 
of  critical  phases.  It  is  evident  that  there  are  only  two  independent 
equations  of  this  character,  as  a  critical  phase  is  capable  oi  n—l  inde- 
pendent variations. 

We  are  not,  however,  absolutely  certain  that  equation  (200)  will 
always  be  satisfied  by  a  critical  phase.  For  it  is  possible  that  the 
denominator  in  the  fraction  may  vanish  as  well  as  the  numerator  for 
an  infinitesimal  change  of  phase  in  which  the  quantities  indicated 
are  constant.  In  such  a  case,  we  may  suppose  the  subscript  n  to 
refer  to  some  different  component  substance,  or  use  another  differen- 
tial coefficient  of  the  same  general  form  (such  as  are  described  on 
page  171  as  characterizing  the  limits  of  stability  in  respect  to  con- 
tinuous changes),  making  the  corresponding  changes  in  (201)  and 
(202).  We  may  be  certain  that  some  of  the  formula^  thus  formed 
will  not  fail.     But  for  a  perfectly  rigorous  method  there  is  an  ad  van- 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Srdistances.      10] 


tage  ill  the  use  of  ;;,  y,  ^jj/n,,  .  .  .  m„  as  independent  variables.  The 
condition  that  the  phase  may  be  vai'ied  without  altering  any  of  the 
quantities  t,  //,,  //.,,  ...//„  will  then  be  expressed  by  the  equation 

i?„+i=0,  (203) 

in  which  /i„^^  denotes  the  same  determinant  as  on  page  169.  To 
obtain  the  second  equation  characteristic  of  critical  phases,  we  observe 
that  as  a  phase  which  is  critical  cannot  become  unstable  when  \aried 
so  that  n  of  the  quantities  ^,  jt),  /<j,  //g?  •  •  •  /'«  remain  constant,  the 
differentia]  of  ^n^.,  for  constant  volume,  viz., 

^-^»+l^„-i-^^-^"+l  dm  .    -U   ^J^  dm„ 

dtn„ 


+ 


(204) 


d//  dm  I 

cannot  become  negative  when  n  of  the  equations  (1V2)  are  satisfied. 
Neither  can  it  have  a  positive  value,  for  then  its  value  might  become 
negative  by  a  change  of  sign  of  d?/,  dm^,  etc.  Therefore  the  expres- 
sion (204)  has  the  value  zero,  if  w  of  the  equations  (172)  are  satisfied. 
This  may  be  expressed  by  an  equation 

aS=0,  (205) 

in  which  S  denotes  a  determinant  in  which  the  constituents  are  the 
same  as  in  ^„+i,  except  in  a  single  horizontal  line,  in  which  the 
differential  coefficients  in  (204)  are  to  be  substituted.  In  whatever 
line  this  substitution  is  made,  the  equation  (205),  as  well  as  (203), 
will  hold  true  of  every  critical  phase  without  exception. 

If  we  choose  t,  p,  m^,  m^,  .  .  .  m„  ?is  independent  variables,  and 
write  V  for  the  determinant 

d^i  dH  dn 


(206) 


and  V  for  the  determinant  formed  from  this  by  substituting  for  the 
constituents  in  any  horizontal  line  the  expressions 

IE,  i^,       .      .     .       i^  (20V) 

the  equations  of  critical  phases  will  be 

Z7=  0,  V—  0.  (208) 

It  results  immediately  from  the  definition  of  a  critical  phase,  that 

an  infinitesimal   change  in   the  condition  of  a  mass  in  such  a  phase 


dm^^ 

dm^dm^ 

dm^.^dm^ 

dn 

dm^dm^ 

dH 
dm^'^ 

dH 
dm„_^  dm^ 

dH 

dH 

dH 

dm ,  dm^^ , 

dm2dmn-^ 

dm„_^^ 

192     J.  TF.  Gibhs — EquiUbrmm  of  Heterogeneous  Substances. 

may  cause  the  mass,  if  it  remains  in  a  state  of  dissipated  energy  (i.  e., 
in  a  state  in  which  the  dissipation  of  energy  by  internal  processes  is 
complete),  to  cease  to  be  homogeneous.  In  this  respect  a  critical  phase 
resembles  any  phase  which  has  a  coexistent  phase,  but  diifers  from 
such  phases  in  that  the  two  parts  into  which  the  mass  divides  when 
it  ceases  to  be  homogeneous  differ  infinitely  little  from  each  other  and 
from  the  original  phase,  and  that  neither  of  these  parts  is  in  general 
infinitely  small.  If  we  consider  a  change  in  the  mass  to  be  deter- 
mined by  the  values  of  dij,  dv,  dtn^,  dm 2,  .  .  .  dw„,  it  is  evident 
that  the  change  in  question  Avill  caiise  the  mass  to  cease  to  be  homo- 
geneous whenever  the  expression 

^f '""-  %  *+  '-i^'  '"'•'  ••■+^17  *""      <^'''> 

has  a  negative  value.  For  if  the  mass  should  remain  homogeneous, 
it  would  become  imstable,  as  Ji„+i  would  become  negative.  Hence, 
in  general,  any  change  thus  determined,  or  its  reverse  (determined  by 
giving  to  dr/,  dv,  dm^,  dm^,  .  .  .  dm„  the  same  values  taken  nega- 
tively), will  cause  the  mass  to  cease  to  be  homogeneous.  The  condi- 
tion which  must  be  satisfied  with  refei'ence  to  dij,  dv,  diit^,  dm^, 
.  .  .  dm„,  in  order  that  neither  the  change  indicated,  nor  the 
reverse,  shall  destroy  the  homogeneity  of  the  mass,  is  expressed  by 
equating  the  above  expression  to  zero. 

But  if  we  consider  the  change  in  the  state  of  the  mass  (supposed  to 
remain  in  a  state  of  dissipated  energy)  to  be  determined  by  arbitrary 
values  of  vi-f  1  of  the  differentials  dt,  dp,  f^/',,  djx^,  .  .  .  dj.i„,  the  case 
will  be  entirely  different.  For,  if  the  mass  ceases  to  be  homogeneous, 
it  will  consist  of  two  coexistent  phases,  and  as  applied  to  these  only 
n  of  the  quantities  t, p,  /<,,  //g,  •  •  .  yw„  will  be  independent.  There- 
fore, for  arbitrary  variations  of  n+l  of  these  quantities,  the  mass 
must  in  general  remain  homogeneous. 

But  if,  instead  of  supposing  the  mass  to  remain  in  a  state  of  dissi- 
pated energy,  we  suppose  that  it  remains  homogeneous,  it  may  easily 
be  shown  that  to  certain  values  of  u-\-l  of  the  above  differentials 
there  will  correspond  three  different  phases,  of  which  one  is  stable 
with  respect  both  to  continuous  and  to  discontinuous  changes,  another 
is  stable  with  respect  to  the  former  and  unstable  with  respect  to  the 
latter,  and  the  third  is  unstable  with  respect  to  both. 

In  general,  however,  if  91  of  the  quantities  p,  t,  /a ^,  /<^,  .  .  .  //„, 
or  n  arbitrary  functions  of  these  quantities,  have  the  same  constant 
values  as  at  a  critical  phase,  the  linear  series  of  phases  thus  deter- 
mined will  be  stable,  in  the  vicinity  of  the  critical  phase.     But  if  less 


J.  W.  Gibbs — Equilibrium,  of  Heterogeneous  Substances.      193 

than  n  of  these  quantities  or  functions  of  tlie  same  together  with  cer- 
tain of  the  quantities  ?;,  u,  wij,  Wj,  .  .  .  m„,  or  arbitrary  functions  of 
the  latter  quantities,  have  the  same  values  as  at  a  critical  phase,  so 
as  to  determine  a  linear  series  of  phases,  the  differential  of  i?„+i  in 
such  a  series  of  phases  will  not  in  general  vanish  at  the  critical  phase, 
so  that  in  general  a  part  of  the  series  will  be  unstable. 

We  may  illustrate  these  relations  by  considering  separately  the 
cases  in  which  n^^\  and  m  =  2.  If  a  mass  of  invariable  composi- 
tion is  in  a  critical  state,  we  may  keep  its  volume  constant,  and 
destroy  its  homogeneity  by  changing  its  entropy  (i.  e,,  by  adding  or 
subtracting  heat — probably  the  latter),  or  we  may  keep  its  entropy 
constant  and  destroy  its  homogeneity  by  changing  its  volume ;  but  if 
we  keep  its  pressure  constant  we  cannot  destroy  its  homogeneity  by 
any  thermal  action,  nor  if  we  keep  its  temperature  constant  can  we 
destroy  its  homogeneity  by  any  mechanical  action. 

When  a  mass  having  two  independently  variable  components  is  in 
a  critical  phase,  and  either  its  volume  or  its  pressure  is  maintained 
constant,  its  homogeneity  may  be  destroyed  by  a  change  of  entropy 
or  temperature.  Or,  if  either  its  entropy  or  its  temperature  is  main- 
tained constant,  its  homogeneity  may  be  destroyed  by  a  .change 
of  volume  or  pressure.  In  both  these  cases  it  is  supposed  that 
the  quantities  of  the  components  remain  unchanged.  But  if  we 
suppose  both  the  temperature  and  the  pressure  to  be  maintained  con- 
stant, the  mass  will  remain  homogeneous,  however  the  proportion  of 
the  components  be  changed.  Or,  if  a  mass  consists  of  two  coexistent 
phases,  one  of  which  is  a  critical  phase  having  two  independently 
variable  components,  and  either  the  temperature  or  the  pressure  of 
the  mass  is  maintained  constant,  it  will  not  be  possible  by  mechanical 
or  thermal  means,  or  by  changing  the  quantities  of  the  components, 
to  cause  the  critical  phase  to  change  into  a  pair  of  coexistent  phases, 
so  as  to  give  three  coexistent  phases  in  the  whole  mass.  The  state- 
ments of  this  paragraph  and  of  the  preceding  have  reference  only  to 
infinitesimal  changes.* 

*  A  brief  abstract  (which  came  to  the  author's  notice  after  the  above  was  in  type) 
of  a  memoir  by  M.  Duolaux,  "  Sur  la  separation  des  liquides  melanges,  etc."  will  be 
found  in  Comptes  Bendus,  vol.  Ixxxi.  (1875),  p.  815. 

Trans.  Conn.  Acad.,  Vol.  III.  26  February,  1876. 


194      J.  W.  Gibbs — Equilibrinm  of  Heterogeneous  Substances. 

ON    THE    VALUES     OF     THE     POTENTIALS    WHEN    THE    QUANTITY    OF    ONE 
OF    THE    COMPONENTS    IS    VERY    SMALL. 

If  Ave  apply  equation  (97)  to  a  homogeneous  mass  having  two  inde- 
pendently variable  components  S^  and  S^,  and  make  t,  p,  and  m, 
constant,  we  obtain 

i'Ilh\  +mrp]  -^0.  (210) 

\dm2/t,p,  m^ 


or 


Therefore,  for  ^2=0,  either 

f^')  =0,  (211) 

/^2\  ^  ^_  (212) 

\dm2}t,p,  7/1, 

Now,  whatever  may  be  the  composition  of  the  mass  considered, 
we  may  always  so  choose  the  substance  S^  that  the  mass  shall  consist 
solely  of  that  substance,  and  in  respect  to  any  other  variable  com- 
ponent S2,  we  shall  have  m2=-0.  But  equation  (212)  cannot  hold 
true  in  general  as  thus  applied.  For  it  may  easily  be  shown  (as  has 
been  done  with  regard  to  the  potential  on  pages  148,  149)  that  the 
value  of  a  diiferential  coefficient  like  that  in  (212)  for  any  given  mass, 
when  the  substance  S^  (to  which  ^3  ^"^^  Ma  relate)  is  determined,  is 
independent  of  the  particular  substance  which  we  may  regard  as  the 
other  component  of  the  mass;  so  that,  if  equation  (212)  holds  true 
when  the  substa.nce  denoted  by  S^  has  been  so  chosen  that  W2=0,  it 
must  hold  true  without  sucli  a  restriction,  Avhich  cannot  generally 
be  the  case. 

In  fact,  it  is  easy  to  prove  directly  that  equation  (211)  will  hold 
ti'ue  of  any  phase  which  is  stalile  in  regard  to  continuous  changes 
and  in  which  m^^^O,  (/^w^g  *'^  capable  of  negative  as  icell  as  positive 
values.  For  by  (171),  in  any  pliase  having  that  kind  of  stability,  //j 
is  an  increasing  function  of  w/ j  when  t,p,  and  m.^  are  regarded  as 
constant.  Hence,  //j  will  have  its  greatest  value  when  the  mass  con- 
sists wholly  of  aSj,  i.  e.,  when  mg^rO.  Therefore,  if  w^2  is  capable 
of  negative  as  well  as  positive  values,  equation  (211)  must  hold  true 
for  rn.^  =  0.  (This  appears  also  from  the  geometrical  representation 
of  potentials  in  the  m-t,  curve.     See  page  177.) 

But  if  Wg  is  capable  only  of  positive  values,  we  can  only  conclude 
from  the  preceding  considerations  that  the  value  of  the  differential 
coefficient  in  (211)  cannot  be  positive.  Nor,  if  we  consider  the  physi- 
cal significance  of  this  case,  viz.,  that  an  increase  of  m.^   denotes  an 


J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.      195 

addition  to  the  mass  in  question  of  a  substance  not  before  contained 
in  it,  does  any  reason  appear  for  supposing  that  this  differential  coeffi- 
cient has  generally  the  value  zero.  To  fix  our  ideas,  let  us  suppose 
that  S^  denotes  water,  and  8^  a  salt  (either  anhydrous  or  any  partic-. 
ular  hydrate).  The  addition  of  the  salt  to  water,  previously  in  a 
state  capable  of  equilibrium  with  vapor  or  with  ice,  will  destroy  the 
possibility  of  such  equilibrium  at  the  same  temperature  and  pressure. 
The  liquid  will  dissolve  the  ice,  or  condense  the  vapor,  which  is 
brought  in  contact  with  it  under  such  circumstances,  which  shows 
that  //j  (the  potential  for  water  in  the  liquid  mass)  is  diminished  by 
the  addition  of  the  salt,  when  the  temperature  and  pressure  are  main- 
tained constant.  Now  there  seems  to  be  no  a  priori  reason  for 
supposing  that  the  ratio  of  this  diminution  of  the  potential  for  water 
to  the  quantity  of  the  salt  which  is  added  vanishes  with  this  quantity. 
We  should  rather  expect  that,  for  small  quantities  of  the  salt,  an 
effect  of  this  kind  would  be  proportional  to  its  cause,  i.  e.,  that  the 
differential  coefficient  in  (211)  would  have  a  finite  negative  value  for 
an  infinitesimal  value  of  m^.  That  this  is  the  case  with  respect  to 
numerous  watery  solutions  of  salts  is  distinctly  indicated  by  the 
experiments  of  Wtillner*  on  the  tension  of  the  vapor  yielded  by  such 
solutions,  and  of  Rtldorfff  on  the  temperature  at  which  ice  is  formed 
in  them ;  and  unless  we  have  experimental  evidence  that  cases  are 
numerous  in  which  the  contrary  is  true,  it  seems  not  unreasonable 
to  assume,  as  a  general  law,  that  when  tn^  has  the  value  zero  and  is 
incapable  of  negative  values,  the  differential  coefficient  in  (211)  will 
have  a  finite  negative  value,  and  that  equation  (212)  will  therefore 
hold  true.  But  this  case  must  be  carefully  distinguished  from  that 
in  which  m^  is  capable  of  negative  values,  which  also  may  be  illus- 
trated by  a  solution  of  a  salt  in  water.  For  tliis  purpose  let  S^ 
denote  a  hydrate  of  the  salt  which  can  be  ciystallized,  and  let  S.-, 
denote  water,  and  let  us  consider  a  liquid  consisting  entirely  of  8^ 
and  of  such  temperature  and  pressure  as  to  be  in  equilibrium  with 
crystals  of  S^.  In  such  a  liquid,  an  increase  or  a  diminution  of  the 
quantity  of  water  would  alike  cause  crystals  of  8^  to  dissolve,  which 
requires  that  the  differential  coefficient  in  (211)  shall  vanish  at  the 
particular  phase  of  the  liquid  for  which  m,  =  0. 

Let  us  return  to  the  case  in  which  m.^\^  incapable  of  negative  values, 
and  examine,  without  other  restriction  in  regard  to  the  substances 

*  Fogg.  Ann.,  vol.  ciii.  (1858),  p.  529 ;  vol.  cv.  (1858),  p.  85;  vol.  ex.  (1860),  p.  564. 
\  Pogg.  Ann.,  vol.  cxiv.  (1861),  p.  63. 


196      J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substa7ices. 

denoted  by  *S'i  and  S^,  the  relation  between  //g  and  ^  tor  any  con- 
stant temperature  and  pressure  and  for  such  small  values   of  -^  that 

the  differential  coefficient  in  (211)  may  be  regarded  as  having  the  same 
constant  value  as  when  m^  =  0,  the  values  of  t,  p,  and  m  ^  being  un- 
changed.    If  we  denote  this  value  of  the  differential  coefficient  by 

—  the  value  of  ^  will  be  positive,  and  will  be  independent  of  m^. 

m^  ' 

Then  for  small  values  of  '^,  we  have  by  (210),  approximately, 


^2 

i.  e., 


^\dm2/t,  p,  m, 
\rtlog  rn2/t,p,  Ml 


If  we  write  the  integral  of  this  equation  in  the  form 

pi2=Alog-^^,  (215) 

J^  like  A  will  have  a  positive  value  depending  only  upon  the  tempera- 
ture and  pressure.  As  this  equation  is  to  be  applied  only  to  cases  in 
which   the  value   of  m^    is   very  small  compared  with   ^)t^,  we  may 

regard  — -  as  constant,  when  temperature  and  pressure  are  constant, 

and  write 

p(^  =  A\og—^,  (216) 

C  denoting  a  positive  quantity,  dependent  only  upon  the  temperature 
and  pressure. 

We  have  so  far  considered  the  composition  of  the  body  as  varying 
only  in  regard  to  the  proj^ortion  of  two  comi^onents.  But  the  argu- 
ment will  be  in  no  respect  invalidated,  if  we  suppose  the  composition 
of  the  body  to  be  capable  of  other  variations.  In  this  case,  the  quan- 
tities A  and  6'  will  be  functions  not  only  of  the  temperature  and 
pressure  but  also  of  the  quantities  which  express  the  composition  of 
the  substance  of  which  together  with  S^  the  body  is  composed.  If 
the  quantities  of  any  of  the  components  besides  yS'a  are  very  small 
(relatively  to  the  quantities  of  others),  it  seems  reasonable  to  assume 
that  the  value  of  ju^,  and  therefore  the  values  of  .1  and  C,  will  be 
nearly  the  same  as  if  these  components  were  absent. 


J.  W.  Gihhs — EquUibriiim  of  Heterogeneous  Substances.      197 

Hence,  if  the  independently  variable  components  of  any  body  are 
aS„,  .  .  .  Sg,  and  S/,,  .  .  .  /iS'^.,  the  quantities  of  the  latter  being  very  small 
as  compared  with  the  quantities  of  the  former,  and  are  incapable  of 
negative  values,  we  may  express  approximately  the  values  of  the 
])otentials  for  S,„  .  .  .  /Si.  by  equations  (subject  of  coui-se  to  the  uncer- 
tainties of  the  assumptions  which  have  been  made)  of  the  form 

M,.=  A,\og^'f^;  (217) 

//,=A•log-^^  (218) 

V 

in  which  A,^,  C\,  .  .  .  A^.,  C^.  denote  functions  of  the  temperature,  the 
pressure,  and  the  ratios  of  the  quantities  ni„,  .  .  .  rn^. 

We  shall  see  hereafter,  when  we  come  to  consider  the  properties  of 
gases,  that  these  equations  may  be  verified  experimentally  in  a  very 
large  class  of  cases,  so  that  we  have  considerable  reason  for  believing 
that  they  express  a  general  law  in  regard  to  the  limiting  values  of 
potentials.* 

ON    CERTAIN    POINTS    KELATING    TO    THE    MOLECULAR    CONSTITUTION     OF 

BODIES. 

It  not  unfrequently  occurs  that  the  number  of  proximate  compo- 
nents which  it  is  necessary  to  recognize  as  independently  variable  in 
a  body  exceeds  the  number  of  components  which  would  be  sufficient 
to  express  its  ultimate  composition.  Such  is  the  case,  for  example,  as 
has  been  remarked  on  page  117,  in  regard  to  a  mixture  at  ordinary 
temperatures  of  vapor  of  water  and  free  hydrogen  and  oxygen. 
This  case  is  explained  by  the  existence  of  three  sorts  of  molecules  in 
the  gaseous  mass,  viz.,  molecules  of  hydrogen,  of  oxygen,  and  of 
hydrogen  and  oxygen  combined.  In  other  cases,  which  are  essentially 
the  same  in  principle,  we  suppose  a  greater  number  of  different  sorts 
of  molecules,  which  differ  in  composition,  and  the  relations  between 

*  The  reader  will  not  fail  to  remark  that,  if  we  could  assume  the  universality  of  this 
law,  the  statement  of  the  conditions  necessary  for  equilibrium  between  different 
masses  in  contact  would  be  much  simplified.  For,  as  the  potential  for  a  substance 
which  is  only  &  possible  component  (see  page  117)  would  always  have  the  value  —  oo^ 
the  case  could  not  6ccur  that  the  potential  for  any  substance  should  have  a  greater 
vakie  in  a  mass  in  which  that  substance  is  only  a  possible  component,  than  in  another 
mass  in  which  it  is  an  actual  component;  and  the  conditions  (22)  and  (51)  might  be 
expressed  with  the  sign  of  equality  without  exception  for  the  case  of  possible 
components. 


198      J.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 

these  may  be  more  complicated.  Other  cases  are  explained  by  mole- 
cules which  differ  in  the  quantity  of  matter  which  they  contain,  but 
not  in  the  kind  of  matter,  nor  in  the  proportion  of  the  different  kinds. 
In  still  other  cases,  there  appear  to  be  different  sorts  of  molecules, 
which  differ  neither  in  the  kind  nor  in  the  quantity  of  matter  which 
they  contain,  but  only  in  the  manner  in  which  they  are  constituted. 
What  is  essential  in  the  cases  referred  to  is  that  a  certain  number  of 
some  sort  or  sorts  of  molecules  shall  be  equivalent  to  a  certain  number 
of  some  other  sort  or  sorts  in  respect  to  the  kinds  and  quantities  of 
matter  which  they  collectively  contain,  and  yet  the  former  shall  never 
be  transformed  into  the  latter  within  the  body  considered,  nor  the 
latter  into  the  former,  however  the  proportion  of  the  numbers  of  the 
different  sorts  of  molecules  may  be  varied,  or  the  composition  of  the 
body  in  other  respects,  or  its  thermodynamic  state  as  represented  by 
temperature  and  pressure  or  any  other  two  suitable  variables,  pro- 
vided, it  may  be,  that  these  variations  do  not  exceed  certain  limits. 
Thus,  in  the  example  given  above,  the  temperature  must  not  be 
raised  beyond  a  certain  limit,  or  molecules  of  hydrogen  and  of  oxygen 
may  be  transformed  into  molecules  of  water. 

The  differences  in  bodies  resulting  from  such  differences  in  the  con- 
stitution of  their  molecules  are  capable  of  continuous  variation,  in 
bodies  containing  the  same  matter  and  in  the  same  thermodynamic 
state  as  determined,  for  example,  by  pressui-e  and  temperature,  as  the 
numbers  of  the  molecules  of  the  different  sorts  are  varied.  These 
differences  are  thus  distinguished  from  those  which  depend  upon  the 
manner  in  which  the  molecules  are  combined  to  form  sensible  masses. 
The  latter  do  not  cause  an  increase  in  the  number  of  variables  in  the 
fundamental  equation ;  but  they  may  be  the  cause  of  different  values 
of  which  the  function  is  sometimes  capable  for  one  set  of  values  of 
the  independent  variables,  as,  for  example,  when  we  have  several 
different  values  of  t,  for  the  same  values  of  ^,  jo,  m^,  ni^,  .  .  .  m„,  one 
perhaps  being  for  a  gaseous  body,  one  for  a  liquid,  one  for  an  amor- 
phous solid,  and  others  for  different  kinds  of  crystals,  and  all  being 
invariable  for  constant  values  of  the  above  mentioned  independent 
variables. 

But  it  must  be  observed  that  when  the  differences  in  the  constitu- 
tion of  the  molecules  are  entirely  determined  by  the  quantities  of 
the  different  kinds  of  matter  in  a  body  with  the  two  variables  which 
express  its  thermodynamic  state,  these  differences  will  not  involve 
any  increase  in  the  number  of  variables  in  the  fundamental  equation. 
For  example,  if  we  should  raise  the  temperature  of  the  mixture  of 


-/  W.  Gibhs — EquiUhriiim  of  Heterogeneoiis  Substcmces.       199 

vapor  of  water  and  free  hydrogen  and  oxygen,  which  we  have  just 
considered,  to  a  point  at  which  the  numbers  of  the]  different  sorts  of 
molecules  are  entirely  determined  by  the  temperature  and  pressure 
and  the  total  quantities  of  hydrogen  and  of  oxygen  which  are  present, 
the  fundamental  equation  of  such  a  mass  would  involve  but  four  inde- 
pendent variables,  which  might  be  the  four  quantities  just  mentioned. 
The  fact  of  a  certain  part  of  the  matter  j^resent  existing  in  the 
form  of  vapor  of  water  would,  of  course,  be  one  of  the  facts  which 
determine  the  nature  of  the  relation  between  ?  and  the  independent 
variables,  which  is  expressed  by  the  fundamental  equation. 

But  in  the  case  first  considered,  in  which  the  quantities  of  the 
different  sorts  of  molecules  are  not  determined  by  the  temperature 
and  pressure  and  the  quantities  of  the  difierent  kinds  of  matter  in  the 
body  as  determined  by  its  ultimate  analysis,  the  components  of  which 
the  quantities  or  the  potentials  appear  in  the  fimdamental  equation 
must  be  those  which  are  detei-mined  by  the  proximate  analysis  of  the 
body,  so  that  the  variations  in  their  quantities,  with  two  variations 
relating  to  the  thermodynamic  state  of  the  body,  shall  include  all  the 
variations  of  which  the  body  is  capable.*  Such  cases  present  no 
especial  difficulty;  there  is  indeed  nothing  in  the  physical  and 
chemical  jiroperties  of  such  bodies,  so  far  as  a  certain  range  of  experi- 
ments is  concerned,  Avhich  is  different  from  what  might  be,  if  the 
proximate  components  were  incapable  of  farther  reduction  or  trans- 
formation. Yet  among  the  the  various  phases  of  the  kinds  of  matter 
concerned,  represented  by  the  different  sets  of  values  of  the  variables 
which  satisfy  the  fundamental  equation,  there  is  a  certain  class  which 
merit  especial  attention.  These  are  the  phases  for  which  the  entropy 
has  a  maximum  value  for  the  same  matter,  as  determined  by  the 
ultimate  analysis  of  the  body,  with  the  same  energy  and  volume.  To 
fix  our  ideas  let  us  call  the  proximate  components  S^,  .  .  .  S„^  and  the 
ultimate  components  S„^  .  .  .  *S/, ;  and  let  m^,  .  .  .  m„  denote  the 
quantities  of  the  former,  and  m„,  .  ,  .  m^,  the  quantities  of  the  latter. 
It  is  evident  that  m^  .  .  .  m^  are  homogeneous  functions  of  the  first 
degree  of  m,,  .  .  .  J7^„;  and  that  the  relations  between  the  substances 
aSj,  .  .  .  /8„  might  be  expressed  by  homogeneous  equations  of  the  first 
degree  between  the  units  of  these  substances,  equal  in  number  to  the 
difference  of  the  numbers  of  the  proximate  and  of  the  ultimate  com- 

*  The  terms  proximate  or  ultimate  are  not  necessarily  to  be  understood  in  an  abso- 
lute sense.  All  that  is  said  here  and  in  the  following  paragraphs  will  apply  to  many 
cases  in  which  components  may  conveniently  be  regarded  as  proximate  or  ultimate, 
which  are  such  only  in  a  relative  sense. 


200       ./  W.  Gihhs — Equilibrium  of  Heterogeneous  Substances. 

ponents.  The  phases  in  question  are  those  for  which  7/  is  a  maximum 
for  constant  values  of  £,  v,  w„,  .  .  .  m,, ;  or,  as  they  may  also  be 
described,  those  for  which  e  is  a  minimum  for  constant  values  of  ?;,  v, 
m„  .  .  .  ni,, ;  or  for  which  'Q  is  a  minimum  for  constant  values  of 
t,  p,  m„,  .  .  .  m,,.  The  phases  which  satisfy  this  condition  may  be 
readily  determined  when  the  fundamental  equation  (which  will  con- 
tain the  quantities  m^,  .  .  .  ni„  or  yWj,  .  .  .  //„,)  is  known.  Indeed  it  is 
easy  to  see  that  we  may  express  the  conditions  which  determine  these 
phases  by  substituting  /<j,  ...//„  for  the  letters  denoting  the  units 
of  the  corresponding  substances  in  the  equations  which  express  the 
equivalence  in  ultimate  analysis  between  these  units. 

These  phases  may  be  called,  with  reference  to  the  kind  of  change 
which  we  are  considering,  phases  of  dissipated  energ}^  That  we 
have  used  a  similar  term  before,  with  reference  to  a  diiferent  kind  of 
changes,  yet  in  a  sense  entirely  analogous,  need  not  create  confusion. 

Tt  is  chai-acteristic  of  these  phases  that  we  cannot  alter  the  values 
of  wij,  .  .  .  Wn  in  any  real  mass  in  such  a  phase,  while  the  volume  of 
the  mass  as  well  as  its  matter  remain  unchanged,  without  diminish- 
in  o-  the  energy  or  increasing  the  entropy  of  some  other  system. 
Hence,  if  the  mass  is  large,  its  equilibrium  can  be  but  slightly  dis- 
turbed by  the  action  of  any  small  body,  or  by  a  single  electric  spark, 
or  by  any  cause  which  is  not  in  some  way  proportioned  to  the  effect 
to  be  produced.  But  when  the  proportion  of  the  proximate  compo- 
nents of  a  mass  taken  in  connection  with  its  temperature  and  pressure 
is  not  such  as  to  constitute  a  phase  of  dissipated  energy,  it  may  be 
possible  to  cause  great  changes  in  the  mass  by  the  contact  of  a  very 
small  body.  Indeed  it  is  possible  that  the  changes  produced  by  such 
contact  may  only  be  limited  by  the  attainment  of  a  phase  of  dissipated 
energy.  Such  a  result  will  probably  be  produced  in  a  fluid  mass  by 
contact  with  another  fliiid  which  contains  molecules  of  all  the  kinds 
which  occur  in  the  first  fluid  (or  at  least  all  those  which  contain 
the  same  kinds  of  matter  which  also  occur  in  other  sorts  of  molecules), 
but  which  differs  from  the  first  fluid  in  that  the  quantities  of  the 
various  kinds  of  molecules  are  entirely  determined  by  the  ultimate 
composition  of  the  fluid  and  its  temperature  and  pressure.  Or,  to 
speak  without  reference  to  the  molecular  state  of  the  fluid,  the  result 
considered  would  doubtless  be  brought  about  by  contact  with  another 
fluid  which  absorbs  all  the  proximate  components  of  the  first, 
S  ...  aS'„,  (or  all  those  betw-ien  which  there  exist  relations  of  equiva- 
lence in  respect  to  their  ultimate  analysis),  independently,  and  with- 
out passive  resistances,  but  for  which  the  phase  is  completely  deter- 


./  W.  Gibhs — Equilibrium  of  Heterogeneous  8ubstcm<:es.      201 

mined  by  its  temperature  and  pressure  and  its  ultimate  composition  (in 
respect  at  least  to  the  particular  substances  just  mentioned).  By  the 
absorption  of  the  substances  8^,  .  .  .  S^  independently  and  without 
passive  resistances,  it  is  meant  that  when  the  absorbing  body  is  in 
equilibrium  with  another  containing  these  substances,  it  shall  be 
possible  by  infinitesimal  changes  in  these  bodies  to  produce  the  ex- 
change of  all  these  substances  in  either  direction  and  independently. 
An  exception  to  the  preceding  statement  may  of  course  be  made  for 
cases  in  which  the  result  in  question  is  prevented  by  the  occurrence  of 
some  other  kinds  of  change ;  in  other  words,  it  is  assumed  that  the 
two  bodies  can  remain  in  contact  preserving  the  properties  which 
have  been  mentioned. 

The  term  catalysis  has  been  applied  to  such  action  as  we  are  con- 
sidering. When  a  body  has  the  property  of  reducing  another,  with- 
out limitation  with  respect  to  the  proportion  of  the  two  bodies,  to  a 
phase  of  dissipated  energy,  in  regard  to  a  certain  kind  of  molecular 
change,  it  may  be  called  a  perfect  catalytic  ar/ent  with  respect  to  the 
second  body  and  the  kind  of  molecular  change  considered. 

It  seems  not  improbable  that  in  some  cases  in  which  molecular 
changes  take  place  slowly  in  homogeneous  bodies,  a  mass  of  which 
the  temperature  and  pressure  are  maintained  constant  will  be  finally 
brought  to  a  state  of  equilibrium  which  is  entirely  determined  by  its 
temperature  and  pressure  and  the  quantities  of  its  ultimate  compo- 
nents, while  the  various  transitory  states  through  which  the  mass 
passes,  (which  are  evidently  not  completely  defined  by  the  quantities 
just  mentioned,)  may  be  completely  defined  by  the  quantities  of  cer- 
tain proximate  components  with  the  temperature  and  pressure,  and 
the  matter  of  the  mass  may  be  brought  by  processes  approximately 
reversible  from  permanent  states  to  these  varioiis  transitory  states. 
In  such  cases,  we  may  form  a  fundamental  equation  with  reference  to 
all  possible  phases,  whether  transitory  or  permanent;  and  we  may 
also  form  a  fundamental  equation  of  different  import  and  containing 
a  smaller  number  of  independent  variables,  which  has  reference  solely 
to  the  final  phases  of  equilibrium.  The  latter  are  the  phases  of  dissi- 
pated energy  (with  reference  to  molecular  changes),  and  when  the 
more  general  form  of  the  fundamental  equation  is  known,  it  will  be 
easy  to  derive  from  it  the  fundamental  equation  for  these  permanent 
phases  alone. 

Now,  as  these  relations,  theoretically  considered,  are  independent 
of  the  rapidity  of  the  molecular  changes,  the  question  naturally  arises, 
whether  in  cases  in  which  we  are  not  able  to  distinguish  such  trausi- 

Trans.  Conn.  Acad.,  Vol.  III.  26  February,  1876. 


202      J.  W.  Gibbs — Equilibrmm  of  Heterogeneous  Substances. 

tory  phases,  they  may  not  still  have  a  theoretical  significance.  If  so, 
the  consideration  of  the  subject  from  this  point  of  view,  may  assist 
us,  in  such  cases,  in  discovering  the  foi-m  of  the  fundamental  equation 
with  reference  to  the  ultimate  components,  which  is  the  only  equation 
required  to  express  all  the  properties  of  the  bodies  which  are  capable 
of  experimental  demonstration.  Thus,  when  the  phase  of  a  body  is 
completely  determined  by  the  quantities  of  n  independently  vari- 
able components,  with  the  temperature  and  pressure,  and  we  have 
reason  to  suppose  that  the  body  is  composed  of  a  greater  number 
n'  of  proximate  components,  which  are  therefore  not  independ- 
ently variable  (while  the  temperature  and  pressure  remain  constant), 
it  seems  quite  possible  that  the  fundamental  equation  of  the  body 
may  be  of  the  same  form  as  the  equation  for  the  phases  of  dissi- 
pated energy  of  analogous  compounds  of  n'  proximate  and  n  ultimate 
components,  in  which  the  proximate  components  are  capable  of 
independent  variation  (without  variation  of  temperature  or  pressure). 
And  if  such  is  found  to  be  the  case,  the  fact  will  be  of  interest  as 
affording  an  indication  concerning  the  proximate  constitution  of  the 
body. 

Such  considerations  seem  to  be  especially  applicable  to  the  very 
common  case  in  which  at  certain  temperatures  and  pressures,  regarded 
as  constant,  the  quantities  of  certain  proximate  components  of  a 
mass  are  capable  of  independent  variations,  and  all  the  phases  pro- 
duced by  these  variations  are  permanent  in  their  nature,  while  at  other 
temperatures  and  pressures,  likewise  regarded  as  constant,  th^  quan- 
tities of  these  proximate  components  are  not  capable  of  independent 
variation,  and  the  phase  may  be  completely  defined  by  the  quantities 
of  the  ultimate  components  with  the  temperature  and  pressure.  There 
may  be,  at  certain  intermediate  temperatures  and  pi*essures,  a  condi- 
tion with  respect  to  the  independence  of  the  proximate  components 
intermediate  in  character,  in  which  the  quantities  of  the  proximate 
components  are  independently  variable  when  we  consider  all  phases, 
the  essentially  transitory  as  well  as  the  permanent,  but  in  which  these 
quantities  are  not  independently  variable  when  we  consider  the 
permanent  phases  alone.  Now  we  have  no  reason  to  believe  that  the 
passing  of  a  body  in  a  state  of  dissipated  energy  from  one  to  another 
of  the  three  conditions  mentioned  has  any  necessary  connection  with 
any  discontinuous  change  of  state.  Passing  the  limit  which  separates 
one  of  these  states  from  another  will  not  therefore  involve  any  dis- 
continuous change  in  the  values  of  any  of  the  quantities  enumerated 
in  (99)-(103)  on  page  143,  if  >y/,,  wig,  .  .  .  m„,  //j,  //g?  •  •  •  yWn  are 


J.  W.  Gi.bbs — Equilibrium  of  Heterogeneous  Substances.      203 

understood  as  always  relating  to  the  ultimate  components  of  the  body. 
Therefore,  if  we  regard  masses  in  the  diiferent  conditions  mentioned 
above  as  having  different  fundamental  equations,  (which  we  may  sup- 
pose to  be  of  any  one  of  the  five  kinds  described  on  page  143,)  these 
equations  will  agree  at  the  limits  dividing  these  conditions  not  only 
in  the  values  of  all  the  variables  which  appear  in  the  equations,  but 
also  in  all  the  difi'erential  coefficients  of  the  first  order  involving  these 
variables.  We  may  illustrate  these  relations  by  supposing  the  values 
of  t,  />,  and  'Q  for  a  mass  in  which  the  quantities  of  the  ultimate  com- 
ponents are  constant  to  be  represented  by  rectilinear  coordinates. 
Where  the  proximate  composition  of  such  a  mass  is  not  determined 
by  t  and  jo,  the  value  of  I  will  not  be  determined  by  these  variables, 
and  the  points  representing  connected  values  of  t,  ^>,  and  ^  will  form 
a  solid.  This  solid  will  be  bounded  in  the  direction  opposite  to  that 
in  which  l  is  measured,  by  a  surface  which  represents  the  phases  of 
dissipated  energy.  In  a  part  of  the  figure,  all  the  phases  thus  repre- 
sented may  be  permanent,  in  another  part  only  the  phases  in  the 
bounding  surface,  and  in  a  third  part  there  may  be  no  such  solid 
figure  (for  any  phases  of  which  the  existence  is  experimentally 
demonstrable),  but  only  a  surface.  This  surface  together  with  the 
bounding  surfaces  representing  phases  of  dissipated  energy  in  the 
parts  of  the  figure  mentioned  above  forms  a  continuous  sheet,  without 
discontinuity  in  regard  to  the  direction  of  its  normal  at  the  limits 
dividing  the  different  parts  of  the  figure  which  have  been  mentioned. 
(There  may,  indeed,  be  different  sheets  representing  liquid  and 
gaseous  states,  etc.,  but  if  we  limit  our  consideration  to  states  of  one 
of  these  sorts,  the  case  will  be  as  has  been  stated.) 

We  shall  hereafter,  in  the  discussion  of  the  fundamental  equations 
of  gases,  have  an  example  of  the  derivation  of  the  fundamental  equa- 
tion for  phases  of  dissipated  energy  (with  respect  to  the  molecular 
changes  on  which  the  proximate  composition  of  the  body  depends) 
from  the  more  general  form  of  the  fundamental  equation. 

THE  CONDITIONS  OF  EQUILIBRIUM  FOR  HETEROGENEOUS  MASSES   UNDER 
THE    INFLUENCE    OF    GRAVITY. 

Let  US  now  seek  the  conditions  of  equilibrium  for  a  mass  of  various 
kinds  of  matter  subject  to  the  influence  of  gravity.  It  will  be  con- 
venient to  suppose  the  mass  enclosed  in  an  immovable  envelop  which 
is  impermeable  to  matter  and  to  heat,  and  in  other  respects,  except 
in  regard  to  gravity,  to  make  the  same  suppositions  as  on  pages  115, 
116.     The  energy  of  the  mass  will  now  consist  of  two  parts,  one  of 


204      ./.  W.  Gibbs — Equilihrmm  of  Heterogeneous  Substances. 

which  depends  upon  its  intrinsic  nature  and  state,  and  the  other  npon 
its  position  in  space.  Let  Dtn  denote  an  element  of  the  mass,  Ds  the 
intrinsic  energy  of  this  element,  h  its  height  aboA'e  a  fixed  horizontal 
plane,  and  g  the  force  of  gravity  ;  then  the  total  energy  of  the  mass 
(when  without  sensible  motions)  will  be  expressed  by  the  formula 

fI)e-\-fghDm.,  (219) 

in  which  the  integrations  include  all  the  elements  of  the  mass  ;  and 
the  general  condition  of  equilibrium  will  be 

dfBe  +  6fg  h  Dm  ^  0,  (220) 

the  variations  being  subject  to  certain  equations  of  condition.  These 
must  express  that  the  entropy  of  the  whole  mass  is  constant,  that  the 
surface  bounding  the  whole  mass  is  fixed,  and  that  the  total  quanti- 
ties of  each  of  the  component  substances  is  constant.  We  shall  sup- 
pose that  there  are  no  otlier  equations  of  condition,  and  that  the 
independently  variable  components  are  the  same  throughout  the 
whole  mass ;  and  we  shall  at  first  limit  ourselves  to  the  consideration 
of  the  conditions  of  equilibrium  with  respect  to  the  changes  which 
may  be  expressed  by  infinitesimal  variations  of  the  quantities  which 
define  the  initial  state  of  the  mass,  without  regarding  the  possibility 
of  the  formation  at  any  place  of  infinitesimal  masses  entirely  different 
from  any  initially  existing  in  the  same  vicinity. 

Let  Z>//,  Dv.,  JJm^,  .  .  .  J)m„  denote  the  entropy  of  the  element 
J)ni,  its  volume,  and  the  quantities  which  it  contains  of  the  various 
components.     Then 

Dm  =  Dm^  .  .  .  +  Dm„,  (221) 

and 

dJ)m=  dBm^  •  •  •  +  ^-Z>m„.  (222) 

Also,  by  equation  (12), 

6D€  =  t  SDrj  —  ^  dUv  +  ju^  SJJm^  .  .  .  -f  yM„  6J)m„.  (223) 
By  these  equations  the  general  condition  of  equilibrium  may  be 
reduced  to  the  form 

ft  SDi]  ~fp  6Dv  +f/i,  SBm^  .  .  .  -f  ///„  dDm„ 

+  fg  6h  Biti  -\-fg h  6 Dm  ^  .  .  .  -\-  fgh  dDm„ ^0.        (224 ) 

Now  it  will  be  observed  that  the  different  equations  of  condition 
affect  different  parts  of  this  condition,  so  that  we  must  have,  sepa- 
rately, 

ft  6Dt]  i  0,     if      fSDt]  =  0  ;  (225) 


./.  W.  Glbbs — Equilibrium,  of  Heterogeneous  Substances.      205 

-fp  6Bv  -\-fg  6h  Urn  ^  0,  (220) 

if  the  bounding  surface  is  unvaried  ; 

y7<i  61>m^  +  fgh  6Bm^  ^0,     if    fSDm^  =  0  ; 


(227) 
y>„  SJ}ni„  +  fg  h  61>m„  ^  0,     if   f  6Dm^  =  0. 

From  (225)  we  may  derive  the  condition  of  thermal  equilibrium, 

«z=  Const.  (328) 

Condition  (226)  is  evidently  the  ordinary  mechanical  condition  of 
equilibrium,  and  may  be  transformed  by  any  of  the  usual  methods. 
We  may,  for  example,  apply  the  formula  to  such  motions  as  might 
take  place  longitudinally  within  an  infinitely  narrow  tube,  terminated 
at  both  ends  by  the  external  surface  of  the  mass,  but  otherwise 
of  indeterminate  form.  If  we  denote  by  m  the  mass,  and  by  v  the 
volume,  included  in  the  part  of  the  tube  between  one  end  and  a 
transverse  section  of  variable  position,  the  condition  will  take  the 
form 

—  fp  ddv  +  fg  Sh  dm  ^  0,  (229) 

in  which  the  integrations  include  the  whole  contents  of  the  tube. 
Since  no  motion  is  possible  at  the  ends  of  the  tube, 

fp  Sdv  +  fdv  dp  =fd{p  Sv)  z=  0,  (230) 

Again,  if  we  denote  by  y  the  density  of  the  fluid, 

dh 
fg  dh  dm  :=fg  -^  Sv  y  dv  =.fg  y  Sv  dh.  (231 ) 

By  these  equations  condition  (229)  may  be  reduced  to  the  form 

fSv  {dp  -{-  g  y  dh)  ^  0.  (232) 

Therefore,  since  Sv  is  arbitrary  in  value, 

dp  =  —  g  y  dh,  (233) 

which  will  hold  true  at  any  point  in  the  tube,  the  difierentials  being 
taken  with  respect  to  the  direction  of  the  tube  at  that  point.  There- 
fore, as  the  form  of  the  tube  is  indeterminate,  this  equation  must 
hold  true,  without  restriction,  throughout  the  whole  mass.  It  evi- 
dently requires  that  the  pressure  shall  be  a  function  of  the  height 
alone,  and  that  the  density  shall  be  equal  to  the  first  derivative  of 
this  function,  divided  by  —  g. 

Conditions  (227)  contain  all  that  is  characteristic  of  chemical 
equilibrium.     To  satisfy  these  conditions  it  is  necessary  and  sufficient 

that 

yu  J  -f-  ^  A  =  Const.  \ 

(2-34) 

//„  -f  gh  =.  Const.  ) 


206      J.  W.  Glbhs — Equilibrium  of  Heterogeneous  Substances. 

The  expressions  /^j,  .  .  .  /^„  denote  quantities  which  we  have  called 
the  potentials  for  the  several  components,  and  which  are  entirely 
determined  at  any  point  in  a  mass  by  the  nature  and  state  of  the 
mass  about  that  point.  We  may  avoid  all  confusion  between  these 
quantities  and  the  potential  of  the  force  of  gravity,  if  we  distinguish 
the  former,  when  necessary,  as  intrinsic  potentials.  The  relations 
indicated  by  equations  (234)  may  then  be  expressed  as  follows : 

When  a  fluid  mass  is  in  equilibrium  under  the  influence  of  gravity^ 
and  has  the  same  independently  variable  components  throughout^  the 
intrinsic  potentials  for  the  several  components  are  constant  in  any 
given  level,  and  diminish  uniformly  as  the  height  increases,  the  differ- 
ence of  the  values  of  the  intrinsic  potential  for  any  component  at  two 
different  levels,  being  equal  to  the  work  done  by  the  force  of  gravity 
when  a  unit  of  matter  falls  from  the  higher  to  the  lower  level. 

The  conditions  expressed  by  equations  (228),  (233),  (234)  are 
necessary  and  sufficient  for  equilibrium,  except  with  respect  to  the 
possible  formation  of  masses  which  are  not  approximately  identical  in 
phase  with  any  previously  existing  about  the  points  where  they  may 
be  formed.  The  possibility  of  such  formations  at  any  point  is  evidently 
independent  of  the  action  of  gravity,  and  is  determined  entirely  by 
the  phase  or  phases  of  the  matter  about  that  point.  The  conditions 
of  equilibrium  in  this  respect  have  been  discussed  on  pages  128-134. 

But  equations  (228),  (233),  and  (234)  are  not  entirely  independent. 
For  with  respect  to  any  mass  in  which  there  are  no  surfaces  of  dis- 
continuity (i.  e.,  surfaces  where  adjacent  elements  of  mass  have  finite 
differences  of  phase),  one  of  these  equations  will  be  a  consequence  of 
the  others.  Thus  by  (228)  and  (234),  we  may  obtain  from  (97), 
which  will  hold  true  of  any  continuous  variations  of  phase,  the  equa- 
tion 

V  dpz^  —  g  {m  J  .  .  .  -f-  m„)  dh  ;  (235) 

or  dp=  -  gy  dh ;  (236) 

which  will  therefore  hold  true  in  any  mass  in  which  equations  (228) 
and  (234)  are  satisfied,  and  in  which  there  are  no  surfaces  of  discon- 
tinuity. But  the  condition  of  equilibrium  expressed  by  equation 
(233)  has  no  exception  with  respect  to  surfaces  of  discontinuity; 
therefore  in  any  mass  in  which  such  surfaces  occur,  it  will  be  necessary 
for  equilibrium,  in  addition  to  the  relations  expressed  by  equations 
(228)  and  (234),  that  there  shall  be  no  discontinuous  change  of  pressure 
at  these  surfaces. 

This  superfluity  in  the  particular  conditions  of  equilibrium  which 
we  have  found,  as  applied  to  a  mass  which  is  everywhere   continuous 


•7.   ]V.  Gibhs — Equllihrimn  of  Heterogeneous  Substances.      20V 

in  phase,  is  due  to  the  fact  that  we  have  made  the  elements  of  volume 
variable  in  position  and  size,  while  the  matter  initially  contained  in 
these  elements  is  not  supposed  to  be  confined  to  them.  Now,  as  the 
different  components  may  move  in  different  directions  when  the 
state  of  the  system  varies,  it  is  evidently  imi)ossible  to  define  the 
elements  of  volume  so  as  always  to  include  the  same  matter ;  we 
must,  therefore,  suppose  the  matter  contained  in  the  elements  of 
volume  to  vary ;  and  therefore  it  would  be  allowable  to  make  these 
elements  fixed  in  space.  If  the  given  mass  has  no  surfaces  of  discon- 
tinuity, this  would  be  much  the  simplest  plan.  But  if  there  are  any 
surfaces  of  discontinuity,  it  will  be  possible  for  the  state  of  the  given 
mass  to  vary,  not  only  by  infinitesimal  changes  of  phase  in  the  fixed 
elements  of  volume,  but  also  by  movements  of  the  surfaces  of  discon- 
tinuity. It  would  therefore  be  necessary  to  add  to  our  general  con- 
dition of  equilibrium  terms  relating  to  discontinuous  changes  in  the 
elements  of  volume  about  these  surfaces, — a  necessity  which  is 
avoided  if  we  consider  these  elements  movable,  as  we  can  then  sup- 
pose that  each  element  remains  always  on  the  same  side  of  the  surface 
of  discontinuity. 

Method  of  treating  the  preceding  jyrohlem^imiiMch  the  elements  of 
volume  are  regarded  as  fixed. 

It  may  be  interesting  to  see  in  detail  how  the  particular  conditions 
of  equilibrium  may  be  obtained  if  we  regard  the  elements  of  volume 
as  fixed  in  position  and  size,  and  consider  the  possibility  of  finite  as 
well  as  infinitesimal  changes  of  phase  in  each  element  of  volume.  If 
we  use  the  character  A  to  denote  the  differences  determined  by  such 
finite  differences  of  phase,  we  may  express  the  variation  of  the  intrin- 
sic energy  of  tlie  whole  mass  in  the  form 

fSBe  +  fABe,  (237) 

in  which  the  first  integral  extends  over  all  the  elements  which  are 
infinitesimally  varied,  and  the  second  over  all  those  which  experience 
a  finite  variation.  We  may  regard  both  integrals  as  extending 
throughout  the  whole  mass,  but  their  values  will  be  zero  except  for 
the  parts  mentioned. 

If  we  do  not  wish  to  limit  ourselves  to  the  consideration  of  masses 
so  small  that  the  force  of  gravity  can  be  regarded  as  constant 
in  direction  and  in  intensity,  we  may  use  T  to  denote  the  potential  of 
the  force  of  gravity,  and  express  the  variation  of  the  part  of  the 
energy  which  is  due  to  gravity  in  the  form 

-y  r  6 Dm  -fT  ADm.  (238) 


20S      J.  W.  Gihhs — EqiiUihvii(m,  of  Heterogeneous  Substances. 

We  shall  then  have,  for  the  general  condition  of  equilihrium, 

fSDe  +  /AUt  -jTSDm  -  fTADm  ^  0  ;  (239) 

and  the  equations  of  condition  will  be 

fSDi^  -\-fADt]  —  0,  (240) 

.         .         .   '    .  .  .    [  (241) 

fdl)m„  +  fABrn^  =  0.  ) 
We  may  obtain  a  condition  of  equilibrium  independent  of  these  equa- 
tions of  condition,  by  subtracting  these  equations,  multiplied  each 
by  an  indeterminate  constant,  from  condition  (239).  If  we  denote 
these  indeterminate  constants  by  T,  31^,  .  ..  M„,  we  shall  obtain 
after  arranging  the  terms 


/ 


SDs  —  T  6Dm  —  TdDtj  -  iHf,  SDm^  .  .  .  ^  M„  6Dm„ 


fADe-TADm  -  TADi]-M^  ADm^  . .  .  -M„dI>m„^o^  (242) 

The  variations,  both  infinitesimal  and  finite,  in  this  condition  are 
independent  of  the  equations  of  condition  (240)  and  (241),  and  are 
only  subject  to  the  condition  that  the  varied  values  of  J)e,  i>//, 
Dm^,  .  .  .  lJm„  for  each  element  are  determined  by  a  certain  change 
of  phase.  But  as  we  do  not  suppose  the  same  element  to  experi- 
ence both  a  finite  and  an  infinitesimal  change  of  phase,  we  must  have 
SJ)e~  FdDm  -  TdBi]  -  31^  SBrn^  .  .  .  -  M„  SBm.„^0,  (243) 

and 
ADs  —  TADm  -  TAD??  —  M^  A  Dm,  ...  -  3/„  JX>w„^0.   (244) 
By  equation  (12),  and  in  virtue  of  the  necessary  relation  (222),  the 
first  of  these  conditions  reduces  to 

{t  —  T)  dDi]  +  (yu,  -  r—  J^/,)  SBm^  .  .  . 

+  (yu„  -  r-  M„)  dDm„^0  ;         (245) 
for  which  it  is  necessary  and  suflicient  that 

t  =  r,  (246) 

V*  (247) 


*  The  gravitation  potential  is  here  supposed  to  be  defined  in  the  usual  way.  But  if 
it  were  defined  so  as  to  decrease  when  a  body  falls,  we  would  have  the  sign  +  instead 
of  —  in  these  equations ;  i.  e.,  for  each  component,  the  sum  of  the  gravitation  and 
intrinsic  potentials  would  be  constant  throughout  the  whole  mass. 


J.  W.  Gibbs — JSquilibHuni  of  Heteroffe)ieous  Substances.      209 

Condition  (244)  may  be  reduced  to  the  form 
ADe^  TJDj]  -  {r-\-M^)JBm,  ..._(]"+  ]\QJJ)m„^0;  (248) 
and  by  (246)  and  (247)  to 

JDe  -  tJDj)  -  //,  JBm^  ...  —  //„  JZ>^/?„^  0.  (249) 

If  values  determined  subsequently  to  the  change  of  phase  are  distin- 
guished by  accents,  this  condition  may  be  written 
J)s'  -  t  Df/  -  //j  Diu^'  ...  -  /.i„Brn„' 

—  Be  +  t  D)i -{- 1.1^  Bm^  ...  +  //„  Bm^  0,         (250) 
which  may  be  reduced  by  (93)  to 

Be'  -  tB)]'  -  //,  Bm^,  ...  -  j.i„Bi>i„'  -]- pBv^O.       (251) 

Now  if  the  element  of  volume  Bv  is  adjacent  to  a  surface  of  discon- 
tinuity, let  us  suppose  Bi\  Bif,  Bm^\  .  .  .  Bm„'  to  be  determined 
(for  the  same  element  of  volume)  by  the  phase  existing  on  the  other 
side  of  the  surface  of  discontinuity.  As  ^,  //,,..  .  //„  have  the  same 
values  on  both  sides  of  this  surface,  the  condition  may  be  reduced  by 
(93)  to 

—  p'Bv  +pBv^O.  (252) 

That  is,  the  pressure  must  not  be  greater  on  one  side  of  a  surface  of 
discontinuity  than  on  the  other. 

Applied  more  generally,  (251)  expresses  the  condition  of  equilibrium 
with  respect  to  the  possibility  of  discontinuous  changes  of  phases  at 
any  point.     As  Bv'  =  Bv,  the  condition  may  also  be  written 

Be'  -  tB}/  +pBij'  -  yt<,  i>m,',  ...  -  u„Bm„'^0,  (253) 
which  must  hold  true  when  t,  p,  /a^,  .  .  .  //„  have  values  determined 
by  any  point  in  the  mass,  and  Ba',  Bt/,  Bv',  Btn^ ,  .  .  .  BmJ,  have 
values  determined  by  any  possible  phase  of  the  substances  of  which 
the  mass  is  composed.  The  application  of  the  condition  is,  however, 
subject  to  the  limitations  considered  on  pages  128-134.  It  may 
easily  be  shown  (see  pages  160,  161)  that  for  constant  values  of  t,  //,, 
.  .  .  //„,  and  of  Bv' ,  the  first  member  of  (253)  will  have  the  least  possi- 
ble value  when  Be',  Bif,  Bm  j ',  .  .  .  Bm^  are  determined  by  a  phase 
for  which  the  temperature  has  the  value  t,  and  the  potentials  the 
values  yt<,,  .  .  .  //„.  It  will  be  sufficient,  therefore,  to  consider  the 
condition  as  applied  to  such  phases,  in  which  case  it  may  be  reduced 
by  (93)  to 

p—p'^O.  (254) 

That  is,  the  pressure  at  any  point  must  be  as  gieat  as  that  of  any 

phase  of  the   same  components,  for  which  the  temperature  and  the 

Trans.  Conn.  Acad.,  Vol.  III.  27  April,  1876. 


210      J.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 

potentials  have  the  same  values  as  at  that  point.  We  may  also 
express  this  condition  by  saying  that  the  pressure  nnist  be  as  great 
as  is  consistent  with  equations  (246),  (247).  This  condition  with  the 
equations  mentioned  will  always  be  sufficient  foi-  equilibrium  ;  when 
the  condition  is  not  satisfied,  if  equilibrium  subsists,  it  will  be  at 
least  practically  unstable- 

Hence,  the  phase  at  any  point  of  a  fluid  mass,  which  is  in  stable 
equilibrium  under  the  influence  of  gravity  (whether  this  force  is  due 
to  external  bodies  or  to  the  mass  itself),  and  which  has  throughout 
the  same  independently  variable  components,  is  completely  deter- 
mined by  the  phase  at  any  other  point  and  the  difierence  of  the 
values  of  the  gravitation  potential  for  the  two  points. 

FUNDAMENTAL    EQUATIONS    OF    IDEAL    GASES    AND    GAS-MIXTUKES. 

For  a  constant  quantity  of  a  perfect  or  ideal  gas,  the  product  of 
the  volume  and  pressure  is  proportional  to  the  temperature,  and  the 
variations  of  energy  are  proportional  to  the  variations  of  tempera- 
ture.    For  a  unit  of  such  a  gas  we  may  write 

p  v:=  a  t^ 
de  z=.  c  dt, 

a  and  c  denoting  constants.     By  integration,  we  obtain  the  equation 

e=  ct+E, 
in  which  S  also  denotes  a  constant.     If  by  these  equations  we  elimin- 
ate t  and  p  from  (11),  we  obtain 

s-E  ,        a    £-E  , 

de  =z d?} dv, 

C  V         c 

or 

d€  ,  dv 

c vt  =  dv  -  (/  — . 

The  integral  of  this  equation  may  be  written  in  the  form 

c  log    =:  //  —  a  log  V  —  JI, 

where  ^denotes  a  fourth  constant.  We  may  regard  ^as  denoting  the 
energy  of  a  unit  of  the  gas  for  ^=0  ;  ^its  entropy  for  ^=1  and  v=zl ; 
a  its  pressure  in  the  latter  state,  or  its  volume  for  t=l  and  p=zl  ; 
c  its  specific  heat  at  constant  volume.  We  may  extend  the  application 
of  the  equation  to  any  quantity  of  the  gas,  without  altering  the 

values  of  the  constants,  if  we  substitute — ,  -,  —  for    e,    ri,    v.  respec- 

m   m   m  i     i->      i        y 

tively.     This  will  give 


J.  W.  Gibbs — B,quilibriu)n  of  Heterogeneous  Substances.      211 

1       £  —  Em        7;       ^_         ,      m  ,       , 

c  loar  =  —  —  H  +  aXocf—.  (255) 

em  in  v 

This  is  a  fundamental  equation  (see  pages  140-144)  for  an  ideal  gas  of 
invariable  composition.  It  Avill  be  observed  that  if  we  do  not  have 
to  consider  the  properties  of  the  matter  which  forms  the  gas  as  ap- 
pearing in  any  other  form  or  combination,  but  solely  as  constituting 
the  gas  in  question  (in  a  state  of  jjurity),  we  may  without  loss  of 
generality  give  to  E  and  H  the  value  zero,  or  any  other  arbitrary 
values.  But  when  the  scope  of  our  investigations  is  not  thus  limited, 
we  may  have  determined  the  states  of  the  substance  of  the  gas  for 
which  ez=:Q  and  ;/=:0  with  reference  to  some  other  form  in  which  the 
substance  appears,  or,  if  the  substance  is  compound,  the  states  of  its 
components  for  which  ez=.0  and  ;/=0  may  be  already  determined ;  so 
that  the  constants  E  and  H  cannot  in  general  be  treated  as  arbitrary. 
We  obtain  from  (255)  by  differentiation 

;         ,  1  ,        <x     ,  /     cE  c+a        f/  \    y 

f^  de=  -dt/ dv  +  ( ^r-  +  — -2    (^ni,       256) 

f^m  m  V  \e  —  Jlini  m         m^/  ' 


8-E'. 

whence,  in  virtue  of  the  general  relation  expressed  by  (86), 

e  —  Em 


c  m 


(257) 


8  — Em  ,  ^  , 

p  =  a ,  (258) 

cv 

u  =  E+  —-^\c  m.  +  a  m  -  ?/).  (259) 

We  may  obtain  the   fundamental  equation  between  //•,  t,  i\  and  ?n 
from  equations  (87),  (255),  and  (257).     Eliminating  £  we  have 
if'  =z  Em  +  c  m  t  —  ^  //, 

and  c  losr  t=: ^  +  « log  -  ; 

and  eliminating  //,  we  have  the  fundamental  equation 

/  m\ 

0  =  Em  ^  mty<-  —  H  -  c  log  t  +  (/  log  -  J.  (260) 

Differentiating  this  equation,  we  obtain 

/                              1        y \    T        amt 
dip  =-  m\H+  cXo^t-^  «log -J  dt ^-  dv 

j.Ie  +  t  Ic  +  <i  -  H  -  c\ogt  +  a  log  '-^1  jdm  •       (261 ) 


212      fT.  W.  Gibhs — Equilibrium  of  Heterogeneous  Substances. 
whence,  by  the  general  equation  (88), 

1]  =  m  { H+  c  log  «;  +  a  log  —  J ,  (262) 

am  t  ,       . 

/>  =  — -  (263) 

c  +  a  -  Il—c\ogt-\-alog  —  \.  (264) 

From  (260),  by  (87)  and  (91),  we  obtain 

'C,  =  Em,  -\-  ')nt\c  —  H  —  c  log  t  +  a  log  —  ]  +  p  v, 

and  eliminating  v  by  means  of  (263),  we  obtain  the  fundamental  equa- 
tion 

?  =  Eyn  +  m  tic  +  a  -  H -  {c-^a)  log  ^  +  a  log  — |.      (265) 

From  this,  by   differentiation    and  comparison   with    (92),  we  may 
obtain  the  equations 

//  z=.  m  (Hi-  (c  +  a)  log  «  —  a  log  —  |,  (266) 

a  m  t 

^=-^,  (267) 

lx  =  E -{-  tic  +  a  —  H -   (e+«)  log  t  +  a  log  —  j.  (268) 

The  last  is  also  a  fundamental  equation.     It  may  be  written  in  the 
form 

or,  if  we  denote  by  e  the  base  of  the  Naperian  system  of  logarithms, 

E—c—a     c  +  a       fi—E 
p  =  ae     "■       t    ""      e     ""^  (270) 

The  fundamental  equation  between   Xi   V-,  Pi   ^"d   m  may  also  be 
easily  obtained  ;   it  is 

(c+«)log7 =--H+a\og^,  (271) 

^         ^     *  {c-\-a)m      m  ^  a'  ^       ' 

which  can  be  solved  with  respect  to  x- 

Any  one  of  the  fundamental   equations   (255),   (260),  (265),  (270), 
and  (271),   which   are   entirely   equivalent  to   one   another,   may  be 


J.  W.  Gibbs — Eqtcilibriuin  of  IJeterogeneoKs  ySiibstances.      213 

regarded  as  defining  an  ideal  gas.     It  will  be  observed  that   most  of 
these  equations  might   be  abbreviated  by  the  use  of  different  con- 
stants.    In    (270),   for  example,  a  single  constant  might  be  used  for 
H—c—a 

— " C -\- €t 

a  e      '^      ,  and  another  for ■  ^       The   equations  have  been    given 

in  the  above  form,  in  order  that  the  relations  between  the  constants 
occurring  in  the  different  equations  might  be  most  clearly  exhibited. 
The  sum  c  +  a  is  the  specific  heat  for  constant  pressure,  as  appears  if  we 
diflerentiate  (266)  regarding  jt>  and  in  as  constant.* 

*  We  may  easily  obtain  the  equation  between  the  temperature  and  pressure  of  a 
saturated  vapor,  if  we  know  the  fundamental  equations  of  the  substance  both  in  the 
gaseous,  and  in  the  liquid  or  solid  state.  If  we  suppose  that  the  density  and  the  specific 
heat  at  constant  pressure  of  the  liquid  may  be  regarded  as  constant  quantities  (for  such 
moderate  pressures  as  the  liquid  experiences  while  in  contact  with  the  vapor),  and 
denote  this  specific  heat  by  A;,  and  the  volume  of  a  unit  of  the  liquid  by  V.  we  shall 
have  for  a  unit  of  the  liquid 

t  dr/  =  k  dt, 
whence 

7]  =  k  log  t  +  H\ 

where  H'  denotes  a  constant.     Also,  from  this  equation  and  (97), 

dfi  —  -  (k  log  t  +  R')dt+V  dp, 
whence 

11  =  kt— kt  log  t—H't+Vp  +  E%  (a) 

where  E'  denotes  another  constant.  This  is  a  fundamental  equation  for  the  substance 
in  the  liquid  state.  If  (268)  represents  the  fundamental  equation  for  the  same  sub- 
stance in  the  gaseous  state,  the  two  equations  will  both  hold  true  of  coexistent  liquid 
and  gas.     Eliminating  u  we  obtain 

p       H—H'  +  k—c—a      k—c—a,  E—E'  V     p 

a                     a                         a                        at  a      t 

If  we  neglect  the  last  term,  which  is  evidently  equal  to  the  density  of  the  vapor 

divided  by  the  density  of  the  liquid,  we  may  write 

C 
log p=A  —  Blog  t -, 

A,  B,  and  C  denoting  constants.  If  we  make  similar  suppositions  in  regard  to  the 
substance  in  the  solid  state,  the  equation  between  the  pressure  and  temperature  of 
coexistent  solid  and  gaseous  phases  wiU  of  course  have  the  same  form. 

A  similar  equation  will  also  apply  to  the  phases  of  an  ideal  gas  which  are  coexis- 
tent with  two  different  kinds  of  solids,  one  of  which  can  be  formed  by  the  combina- 
tion of  the  gas  with  the  other,  each  being  of  invariable  composition  and  of  constant 
specific  heat  and  density.     In  this  case  we  may  write  for  one  solid 
/x ,  --  k't-k't  log  t- H't  +  V'p  +  E', 

and  for  the  other 

ji.,  =  k"t-k"t  log  t-H"t+  V"p  +  E", 

and  for  the  gas 

^;,  =  E-^t(c  +  a-H—  (c  +  a)  log  f  +  a  log  — j. 


214      J.  W.  Gibbs — Equilibriiini  of  Heterogeneous  Substances. 

The  preceding  fundamental  equations  all  apply  to  gases  of  constant 
composition,  for  which  the  matter  is  entirely  determined   by  a  single 


Now  if  a  unit  of  the  gas  unites  with  the  quantity  /i  of  the  first  solid  to  form  the 
quantity  \  +  l  of  the  second  it  will  be  necessary  for  equilibrium  (see  pages  121,  122) 

that 

^3+A^,  =(1  +A)//.,. 

Substituting  the  values  of  /i,,  //._,,   //;j,   given  above,   we  obtain  after  arranging  the 
terms  and  dividing  by  at 


when 


loo;  —  =  A-  Bios  t +  D  — , 

^   a  ^  t  I  ' 


_  H+AH'-{l+l)H"-c-a-lk'  +  {l  +  'A)k' 


„      (WA)Jc"-lk'-c~a 
a 

E+lE'-{\+l)E"  (1+A)F"-AF' 

0  — ,  L)  —     ■ . 

a  a 

We  may  conclude  from  this  that  an  equation  of  the  same  form  may  be  applied  to 
an  ideal  gas  in  equilibrium  with  a  liquid  of  wliich  it  forms  an  independently  variable 
component,  wlien  the  specific  heat  and  density  of  the  liquid  are  entirely  determined 
by  its  composition,  except  that  the  letters  A.  B,  C,  and  D  must  in  this  case  be  under- 
stood to  denote  quantities  which  vary  with  the  composition  of  the  liquid.  But  to 
consider  the  case  more  in  detail,  we  have  for  the  liquid  by  (a) 

-  -  —u=ki-kt  loo;  t-H't+  Vp  +  E', 
m 

where  k,  H%   V,  E'  denote  quantities  which  depend  only  upon  the  composition  of  the 
liquid.     Hence,  we  may  write 

C  =  bt-kt  log  (~m  +  V])  +  E, 

where  k,  H,  V,  and  B  denote  functions  of  m^,  rwj,  etc.  (the  quantities  of  the  several 

components  of  the  liquid).     Hence,  by  (92), 

dk  ^       dk    ,  dH.         dV  dE 

// ,  =  ^T—t-  -—t log  If  —  -- — 1+  -^—2}+  1—  . 
am  I        dm,  dm-i       dm,         dm, 

If  the  component  to  which  this  potential  relates  is  that  which  also  forms  the  gas,  we 
shall  have  by  (269) 

•p       H—c—a      c  +  a,  /"j— -^ 

log  ^  = +  log  t+'-^-- . 

a  a  a  at 

Eliminating  /^  i ,  we  obtain  the  equation 

log^=^-51ogi-y+  i>-y-, 

in  which  A,  B,  C,  and  D  denote  quantities  which  depend  only  upon  the  composition 

of  the  liquid,  viz : 

\  I         d-H.  rfk 

A  =  —[  H- c-a-\-^,— 

a  \         dm,  dm,. 


B=L(^-c-a) 

a  \dm,  )' 


J.  W.  Gibhs — Equilihi'mDi  of  Heterogeneous  Substances.      215 

variable  (m).  We  may  obtain  correspoiulincj  fundamental  equations 
for  a  mixture  of  gases,  in  which  the  proportion  of  the  components 
shall  be  variable,  from  the  following  considerations. 

It  is  a  rule  which  admits  of  a  very  general  and  in  many  cases  very 
exact  experimental  verification,  that  if  several  liquid  or  solid  sub- 
stances which  yield  difi^erent  gases  or  vapors  are  simultaneously  in 
equilibrium  with  a  mixture  of  these  gases  (cases  of  chemical  action 
between  the  gases  being  excluded,)  the  pressure  in  the  gas-mixture 
is  equal  to  the  sum  of  the  pressures  of  the  gases  yielded  at  the  same 
temperature  by  the  various  liquid  or  solid  substances  taken  separately. 
Now  the  potential  in  any  of  the  liquids  or  solids  for  the  substance 
which  it  yields  in  the  form  of  gas  has  very  nearly  the  same  value 
when  the  liquid  or  solid  is  in  equilibrum  with  the  gas-mixture  as 
when  it  is  in  equilibrium  with  its  own  gas  alone.  The  difference  of 
the  pressure  in  the  two  cases  will  cause  a  certain  difference  in  the 
values  of  the  potential,  but  that  this  difference  will  be  small,  we  may 
infer  from  the  equation 

C^)  =(,*)  ,  (272) 

\  dp  ft,  m  \dm^lt,p,m  ^ 

which  may  be  derived  from  equation  (92).  In  most  cases,  there  will 
be  a  certain  absorption  by  each  liquid  of  the  gases  yielded  by  the 
others,  but  as  it  is  well  known  that  the  above  rule  does  not  apply  to 
cases  in  which  such  absorption  takes  place  to  any  great  extent,  we 
may  conclude  that  the  effect  of  this  circumstance  in  the  cases  with 
which  we  have  to  do  is  of  secondary  importance.  If  we  neglect  the 
slight  differences  in  the  values  of  the  potentials  due  to  these  cii-cum- 
stances,  the  rule  may  be  expressed  as  follows : 

The  pressure  in  a  mixture  of  different  gases  is  equal  to  the  sum  of 
the  pressures  of  the  different  gases  as  existing  each  by  itself  at  the 
same  temperature  avid  with  the  same  value  of  its  potential. 

To  form  a  precise  idea  of  the  practical  significance  of  the  law  as 
thus  stated  with  reference  to  the  equilibrium  of  two  liquids  with  a 
mixture  of  the  gases  which  they  emit,  when  neither  liquid  absorbs  the 
gas  emitted  by  the  other,  we  may  imagine  a  long  tube  closed  at  each 
end  and  bent  in  the  form  of  a  W  to  contain  in  each  of  the  descending 


C=  -  (^-y-l  ^=-  ^      • 

a  \       dm  I  /  a  am , 

With  respect  to  some  of  the  equations  which  have  here  been  deduced,  the  reader 
may  compare  Professor  Kirchhoff  "  Ueber  die  Spannung  des  Dampfes  von  Mischungen 
aus  Wasser  und  Schwefelsaure,"  Pogg.  Ann.,  vol.  civ.  (18.58),  p.  612  ;  and  Dr.  Raukine 
"On  Saturated  Vapors,''  Phil.  Mag.,  vol.  xxxi.  (1866),  p.  199. 


216      J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances. 

loops  one  of  the  liquids,  and  above  these  liquids  the  gases  which  they 
emit,  viz.,  the  separate  gases  at  the  ends  of  the  tube,  and  the  mixed 
gases  in  the  middle.  We  may  suppose  the  whole  to  be  in  equilibrium, 
the  difference  of  the  pressures  of  the  gases  being  balanced  by  the 
proper  heights  of  the  liquid  columns.  Now  it  is  evident  from  the 
principles  established  on  pages  203-210  that  the  potential  for  either 
gas  will  have  the  same  value  in  the  mixed  and  in  the  separate  gas 
at  the  same  level,  and  therefore  according  to  the  rule  in  the  form 
which  we  have  given,  the  pressure  in  the  gas-mixture  is  equal  to  the 
sum  of  the  pi'essures  in  the  separate  gases,  a/^  (^Aese  joressiwes  being 
measured  at  the  same  level.  Now  the  experiments  by  which  the  rule 
has  been  established  relate  rather  to  the  gases  in  the  vicinity  of  the 
surfaces  of  the  liquids.  Yet,  although  the  differences  of  level  in  these 
surfaces  may  be  considerable,  the  corresponding  differences  of  pres- 
sure in  the  columns  of  gas  will  certainly  be  very  small  in  all  cases 
which  can  be  I'egarded  as  falling  under  the  laws  of  ideal  gases,  for 
which  very  great  pressures  are  not  admitted. 

If  we  apply  the  above  law  to  a  mixture  of  ideal  gases  and  distin- 
guish by  subscript  numerals  the  quantities  relating  to  the  different 
gases,  and  denote  by  ^'^  the  sum  of  all  similar  terms  obtained  by 
changing  the  subscript  numerals,  we  shall  have  by  (270) 

-ff,  — Cj— a,       Ci+a,      fi^—E, 

(a,  a,  ttit      \ 

,      a^  e  t  e  /,  (273) 

It  will  be  legitimate  to  assume  this  equation  provisionally  as  the 
fundamental  equation  defining  an  ideal  gas-mixture,  and  afterwards 
to  justify  the  suitableness  of  such  a  definition  by  the  properties  which 
may  be  deduced  from  it.  In  particular,  it  will  be  necessary  to  show 
that  an  ideal  gas-mixture  as  thus  defined,  when  the  proportion  of  its 
components  remains  constant,  has  all  the  properties  which  have 
already  been  assumed  for  an  ideal  gas  of  invariable  composition ;  it 
will  also  be  desirable  to  consider  more  rigorously  and  more  in  detail 
the  equilibrium  of  such  a  gas-mixture  with  solids  and  liquids,  with 
respect  to  the  above  rule. 

By  differentiation  and  comparison  with  (98)  we  obtain 


=  ^^\  («,+«,-  ^-7—^)  e  t      e  ;,    (274) 

V  t 


J.  W.  Gihhs — Eqidllhriiua  of  Iltterogeneous  /Substances.      2  I  7 


H-i—Cj—a.,       c^     l^i—E.2        )■ 


etc. 


(275) 


Equations  (275)  indicate  that  the  relation  between  the  temperature, 
the  density  of  any  compcfnent,  and  the  potential  for  that  component,  is 
not  aifected  by  the  presence  of  the  other  components.  They  may 
also  be  written 

etc.  ) 


Eliminating  yu,,  /<2,  etc.  from  (273)  and   (274)    by  means  of  (275) 
and  (276),  we  obtain 


(277) 


7=  ^lyn^ir^  +M,c,log  «+m,«ilog  ^j. 


(278) 


E({uation  (277)  expresses  the  familiar  principle  that  the  pressure  in  a 
gas-mixture  is  equal  to  the  sum  of  the  pressures  which  the  component 
gases  would  possess  if  existing  separately  with  the  same  volume  at 
the  same  temperature.  Equation  (278)  expresses  a  similar  principle 
in  regard  to  the  entropy  of  the  gas-mixture. 

From  (276)  and  (277)  we  may  easily  obtain  the  fundamental  equa- 
tion between  //',  t,  v,  m^^  ni^,  etc.  For  by  substituting  in  (94)  the 
values  of  jo,  ji^,  /.i^,  etc.  taken  from  these  equations,  we  obtain 

'p=2^(^£.\m,-\-m^t  |  c, -^, -c.log  «  +  «,log  "^j).    (279) 

If  we  regard  the  proportion  of  the  various  components  as  constant, 
this  equation  may  be  simplified  by  writing 

m    for    ^j  wZj, 
c  m    for    ^  J  (c ,  m  J ), 
am    for    2^  (a^m^), 
Em    for    ^j  (£',  mj), 
and  Hm-am  log  m    for    ^j  (H^  m^—a^  m^  log  rn^). 

The  values  of  c,  a,  -E,  and  JT,  will  then  be  constant  and  m  will  denote 
the  total  quantity  of  gas.     As  the  equation  Avill  thus  be  reduced  to  the 
Trans.  Conn.  Acad.,  Vol.  III.  28  April,  1876. 


218     (./.  W.  (jribhs — Equilibrkiiu  of  Heterogeneous  Suhstances. 

form  of  (260),  it  is  evident  that  an  ideal  gas-mixture,  as  defined  by 
(278)  or  (279),  when  the  proportion  of  its  components  remains  un- 
changed, will  have  all  the  properties  which  we  have  assumed  for  an 
ideal  o-as  of  invariable  composition.  The  relations  between  the  specific 
heats  of  the  gas-mixture  at  constant  volume  and  at  constant  pressure 
and  the  specific  heats  of  its  components  are  expressed  by  the  equations 

c  =  ^'^-\  (280) 

m 

and 

,;^_«=^'  !!hj£i+^.  (281) 

We  have  already  seen  that  the  values  of  t,  v,  m^,  /.i^  in  a  gas- 
mixture  are  such  as  are  possible  for  the  component  G^  (to  which 
/«j  and  /<j  relate)  existing  separately.  If  we  denote  by  jOj,  j/^,  //'j, 
£,,  ^'j,  Cj  the  connected  values  of  the  several  quantities  which  the 
letters  indicate  determined  for  the  gas  6^j  as  thus  existing  sepa- 
rately, and  extend  this  notation  to  the  other  components,  we  shall 
have  by  (273),  (274),  and  (279) 

whence  by  (87),  (89),  and  (91) 

The  quantities  p,  //,  '/',  €,  j,  ?  relating  to  the  gas-mixture  may 
therefore  be  regarded  as  consisting  of  parts  which  may  be  attrib- 
uted to  the  several  components  in  such  a  manner  that  between  the 
parts  of  these  quantities  which  are  assigned  to  any  component,  the 
quantity  of  that  component,  the  potential  for  that  component,  the 
temperature,  and  the  volume,  the  same  relations  shall  subsist  as  if 
that  component  existed  separately.  It  is  in  this  sense  that  we 
should  understand  the  law  of  Dalton,  that  every  gas  is  as  a  vacuum 
to  every  other  gas. 

It  is  to  be  remarked  that  these  relations  are  consistent  and  pos- 
sible for  a  mixture  of  gases  which  are  not  ideal  gases,  and  indeed 
without  any  limitation  in  regard  to  the  thei'modynamic  properties  of 
the  individual  gases.  They  are  all  consequences  of  the  law  that  the 
pressure  in  a  mixtuz-e  of  dilFerent  gases  is  equal  to  the  sum  of  the 
pressures  of  the  different  gases  as  existing  each  by  itself  at  the  same 
tempei'ature  and  with  the  same  value  of  its  potential.  For  let 
Pii  V\i  ^n  '/'i'  /I'l'  ^1  '  P2->  etc.;  etc.  be  defined  as  relating  to  the 
different  gases  existing  each  by  itself  with  the  same  volume,  tem- 
perature, and  potential  as  in  the  gas-mixture ;  if 


'/=-i'/n 

t=^^'/\^, 

(282) 

") 

x=^ai^ 

'^  =  ^\'ii- 

(283) 

./  W.  (jTibhs — EquUlbrlwn  of  Heteroyeneoas  ISuhstaHceti.       219 

the,,  l^\  =iP): 

and  therefore,  by  (98),  the  quantity  of  any  component  gas  <t  ^  in  tlie 
gas-mixture,  and  in  the  separate  gas  to  which  p^,  //j,  eic.  relate,  is 
the  same  and  may  be  denoted  by  the  same  symbol  )ii ^.     Also 

whence  also,  by  (93)-(96), 

All  the  same  relations  will  also  hold  true  whenever  the  value  of  t/^ 
for  the  gas-mixture  is  equal  to  the  sum  of  the  values  of  this  func- 
tion for  the  several  component  gases  existing  each  by  itself  in 
the  same  quantity  as  in  the  gas-mixture  and  with  the  temperature 
and  volume  of  the  gas-mixture.  For  if  ^^j,  //j,  fj,  i/\,  Xi->  ^i  ?  2^21 
etc. ;  etc.  are  defined  as  relating  to  the  components  existing  thus 
by  themselves,  we  shall  have 

'I- =^  lip  I, 
whence 


\drn^  /i,  V,  m        \dm^  ft,  v 


Therefore,  by  (88),  the  potential  //j  has  the  same  value  in  the  gas- 
mixture  and  in  the  gas  G^  existing  separately  as  supposed.  More- 
over, 

'^=^  idiJv,  nT  ~  ^A~df)v,  ra  "  ^'^'^^' 

whence 

Whenever  different  bodies  are  combined  without  communication  of 
work  or  heat  between  them  and  external  bodies,  the  energy  of  the 
body  formed  by  the  combination  is  necessarily  equal  to  the  sum  of  the 
energies  of  the  bodies  combined.  In  the  case  of  ideal  gas-mixtures, 
when  the  initial  temperatures  of  the  gas-masses  which  are  combined 


*  A  subscript  m  after  a  differential  coefficient  relating  to  a  body  having  several 
independently  variable  components  is  used  here  and  elsewhere  in  this  paper  to  indi- 
cate that  each  of  the  quantities  m^,m2,  etc.,  unless  its  differential  occurs  in  the 
expression  to  which  the  suffix  is  applied,  is  to  be  regarded  as  constant  in  the  differ- 
entiation. 


220      J.   W.   Gibbs — Equilibrium,  of  Heterogeneous  Substances. 

are  the  same,  (whether  these  gas-masses  are  entirely  different  gases, 
or  gas-mixtures  differing  only  in  the  proportion  of  their  components,) 
the  condition  just  mentioned  can  only  be  satisfied  when  the  tempera- 
ture of  the  resultant  gas-mixture  is  also  the  same.  In  such  com- 
binations, therefore,  the  final  temperature  will  be  the  same  as  the 
initial. 

If  we  consider  a  vertical  column  of  an  ideal  gas-mixture  which  is 
in  equilibrium,  and  denote  the  densities  of  one  of  its  components  at 
two  different  points  by  y^  and  ;//,  we  shall  have  by  (275)  and  (234) 

i^i-/"/         g[h'-h) 
^=e      "'*     =e    ""'*     .  (284) 

From  this  equation,  in  which  we  may  regard  the  quantities  distin- 
guished by  accents  as  constant,  it  appears  that  the  relation  between 
the  density  of  any  one  of  the  components  and  the  height  is  not 
affected  by  the  presence  of  the  other  components. 

The  work  obtained  or  expended  in  any  reversible  process  of  com- 
bination or  separation  of  ideal  gas-mixtures  at  constant  temperature, 
or  when  the  temperatures  of  the  initial  and  final  gas-masses  and  of 
the  only  external  source  of  heat  or  cold  which  is  used  are  all  the  same, 
will  be  found  by  taking  the  difference  of  the  sums  of  the  values  of  ip 
for  the  initial,  and  for  the  final  gas-raasses.  (See  pages  145,  146). 
It  is  evident  from  the  form  of  equation  (279)  that  this  work  is  equal 
to  the  sum  of  the  quantities  of  work  which  would  be  obtained  or 
expended  in  producing  in  each  different  component  existing  separately 
the  same  changes  of  density  which  that  component  experiences  in 
the  actual  process  for  which  the  w^ork  is  sought.* 

We  will  now  return  to  the  consideration  of  the  equilibrium  of  a 
liquid  with  the  gas  which  it  emits  as  affected  by  the  presence  of 
difterent  gases,  when  the  gaseous  mass  in  contact  with  the  liquid  may 
be  regarded  as  an  ideal  gas-mixture. 

It  may  first  be  observed,  that  the  density  of  the  gas  which  is 
emitted  by  the  liquid  will  not  be  affected  by  the  presence  of  other 
gases  which  are  not  absorbed  by  the  liquid,  when  the  liquid  is  pro- 
tected in  any  way  from  the  pressure  due  to  these  additional  gases. 
This  may  be   accomplished  by   separating  the  liquid   and   gaseous 

*  This  result  has  been  given  by  Lord  Rayleigh,  (Phil.  Mag.,  vol.  xlix,  1875,  p.  311). 
It  will  be  observed  that  equation  (279)  might  be  deduced  immediately  from  this 
principle  in  connection  with  equation  (260)  which  expresses  the  properties  ordinarily 
assumed  for  perfect  gases. 


./  W.  Gibbs — Equilibrmm  of  Heterogeneous  Substances.      221 

masses  by  a  diaphragm  which  is  permeable  to  the  liquid.  It  will 
tlien  be  easy  to  maintain  the  liquid  at  any  constant  pressure  which  is 
not  greater  than  that  in  the  gas.  The  potential  in  the  liquid  for  the 
substance  which  it  yields  as  gas  will  then  remain  constant,  and  there- 
fore the  potential  for  the  same  substance  in  the  gas  and  the  density 
of  this  substance  in  the  gas  and  the  part  of  the  gaseous  pressure 
due  to  it  will  not  be  affected  by  the  other  components  of  the  gas. 

But  when  the  gas  and  liquid  meet  under  ordinary  circumstances, 
i.  e.,  in  a  free  plane  s\irfi\ce,  the  pressure  in  both  is  necessarily  the 
same,  as  also  the  value  of  the  potential  for  any  common  component 
aSj.  Let  us  suppose  the  density  of  an  insoluble  component  of  the  gas 
to  vary,  while  the  composition  of  the  liquid  and  the  temperature 
remain  unchanged.  If  we  denote  the  increments  of  pressure  and  of 
the  potential  for  S^  by  djj  and  c?/<j,  we  shall  have  by  (272) 

\dp  lt,m  \dmjt,p,m 

the  index  (l)  denoting  that  the  expressions  to  which  it  is  affixed  refer 
to  the  liquid.  (Expressions  without  such  an  index  will  refer  to  the 
gas  alone  or  to  the  gas  and  liquid  in  common.)  Again,  since  the  gas 
is  an  ideal  gas-mixture,  the  relation  between  p^  and  /u^  is  the  same 
as  if  the  component  aS'j  existed  by  itself  at  the  same  temperature, 
and  therefore  by  (268) 

(///  J  =  a  J  t  d  log  p^. 
Therefore 

(dv  \^^^ 
- —  I  dp.  (285) 

dmjt,p,m    ^ 

This  may  be  integrated  at  once  if  we  regard  the  differential  coeffi- 
cient in  the  second  member  as  constant,  which  will  be  a  very  close 
approximation.  We  may  obtain  a  result  more  simple,  but  not  quite 
so  accurate,  if  we  write  the  equation  in  the  form 

-^  dp,  (286) 

dm  ^  ft,  2),  m 

where  ;/j  denotes  the  density  of  the  component  /S^  in  the  gas,  and 
integrate  regarding  this  quantity  also  as  constant.     This  wdll  give 

where  jt?/  and  p/  denote  the  values  of  ^j  and  p  -when  the  insoluble 
component  of  the  gas  is  entirely  wanting.  It  will  be  observed  that 
p—p'  is  nearly  equal  to  the  pressure  of  the  insoluble  component,  in 
the  phase  of  the  gas-mixture  to  which  pi   relates.     /S',  is  not  neces- 


222      J.    W.  Gibbs — Equilibrmm  of  Heterogeneous  Substances. 

sarily  the  cmly  common  component  of  the  gas  and  liquid.  If  there 
are  others,  we  may  find  the  increase  of  the  part  of  the  pressure  in  the 
gas-mixture  belonging  to  any  one  of  them  by  equations  differing  from 
the  last  only  in  the  subscript  numerals. 

Let  us  next  consider  the  effect  of  a  gas  which  is  absorbed  to  some 
extent,  and  which  must  therefore  in  strictness  be  regarded  as  a  com- 
ponent of  the  liquid.  We  may  commence  by  considering  in  general 
the  equilibrium  of  a  gas-mixture  of  two  components  /8,  and  IS^  with  a 
liquid  formed  of  the  same  components.  Using  a  notation  like  the 
previous,  we  shall  have  by  (98)  for  constant  temperature, 

and 

dp  =  y^^^  di.i^-\-yf^  dji^  ; 
whence 

Now  if  the  gas  is  an  ideal  gas-mixture, 

a.t  -,         dp.  -,  ,  a^t   ^  dp„ 

du.=i  —^  dpx-=.  -^-',  and  au^  =i  — ^  rt»,  =  -=-^, 

^'        Pv  Vx  Pz  72 

therefore 

l^-\]^dp,=  [\-^^l  dp^.  (288) 

We  may  now  suppose  that  S^  is  the  principal  component  of  the 
liquid,  and  aS's  is  a  gas  which  is  absorbed  in  the  liquid  to  a  slight 
extent.  In  such  cases  it  is  well  known  that  the  ratio  of  the  densities 
of  the  substance  S2  in  the  liquid  and  in  the  gas  is  for  a  given  tem- 
perature approximately  constant.  If  we  denote  this  constant  by  A, 
we  shall  have 

^r.L-  ^^^dp^={\-A)dp^.  (289) 

It  would  be  easy  to  integrate  this  equation  regarding  ;/  j  as  variable, 
but  as  the  variation  in  the  value   of  »,   is  necessarily  very  small  we 

(L) 

shall  obtain  sufficient  accuracy  if  we  regard  }^i  as  well  as  ;(/i  as  con- 
stant.    We  shall  thus  obtain 

(^'^-l)(/>,-^p,')=(l-^)i5„  (290) 

where  ^1' denotes  the  pressure  of  the  saturated  vapor  of  the  pure 
liquid  consisting  of  S^.  It  will  be  observed  that  when  ^=1,  the 
presence  of  the  gas  S^  will  not  affect  the  pressure  or  density  of  the 
gas  S^.  When  ^<^1,  the  pressure  and  density  of  the  gas  S^  are 
greater  than  if  S.^  were  absent,  and  when  A^\,  the  revei-se  is  true. 


./.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances.      223 

The  properties  of  an  ideal  gas-mixture  (according  to  the  definition 
which  we  have  assumed)  when  in  equilibrium  with  liquids  or  solids 
have  been  developed  at  length,  because  it  is  only  in  respect  to  these 
properties  that  there  is  any  variation  from  the  properties  usually 
attributed  to  perfect  gases.  As  the  pressure  of  a  gas  saturated  with 
vaporis  usually  given  as  a  little  less  than  the  sum  of  the  pressure  of  the 
gas  calculated  from  its  density  and  that  of  saturated  vapor  in  a  space 
otherwise  empty,  while  oxir  formulae  would  make  it  a  little  more,  when 
the  gas  is  insoluble,  it  would  appear  that  in  this  respect  our  formulae 
are  less  accurate  than  the  rule  which  would  make  the  pressure  of  the 
gas  saturated  with  vapor  equal  to  the  sum  of  the  two  pressures 
mentioned.  Yet  the  reader  will  observe  that  the  magnitude  of  the 
quantities  concerned  is  not  such  that  any  stress  can  be  laid  upon 
this  circumstance. 

It  will  also  be  observed  that  the  statement  of  Dalton's  law  which  we 
have  adopted,  while  it  serves  to  complete  the  theory  of  gas-mixtui-es 
(with  respect  to  a  certain  class  of  properties),  asserts  nothing  with 
reference  to  any  solid  or  liquid  bodies.  But  the  common  rule  that 
the  density  of  a  gas  necessary  for  equilibrium  with  a  solid  or  liquid 
is  not  altered  by  the  presence  of  a  different  gas  which  is  not  absorbed 
by  the  solid  or  liquid,  if  construed  strictly.,  will  involve  consequences 
in  regard  to  solids  and  liquids  which  are  entirely  inadmissible.  To 
show  this,  we  will  assume  the  correctness  of  the  rule  mentioned.  Let 
aS'j  denote  the  common  component  of  the  gaseous  and  liquid  or  solid 
masses,  and  /Sg  the  insoluble  gas,  and  let  quantities  relating  to  the 
gaseous  mass  be  distinguished  when  necessary  by  the  index  (g),  and 
those  relating  to  the  liquid  or  solid  by  the  index  (l).  Now  while  the 
gas  is  in  equilibrium  with  the  liquid  or  solid,  let  the  quantity  which 
it  contains  of  ^'2  receive  the  increment  dm^.,  its  volume  and  the 
quantity  which  it  contains  of  the  other  component,  as  well  as  the 
temperature,  remaining  constant.  The  potential  for  S^  in  the  gaseous 
mass  will  receive  the  increment 

\ani2l  t,  V,  m 
and  the  pressure  will  receive  the  increment 


\dm. 


I  dnic 


[dm 2  ft,  V,  m 

Now  the  liquid  or  solid  remaining  in  equihbrium  with  the  gas  must 
experience  the  same  variations  in  the  values  of  /u  j  and  p.     But  by  (272) 


\  dpJt,m         \dmjt,j>, 


224      J.  W.  Gibbs — Equilibrium  of  Heterogeneous  ISubstances. 
Therefore, 


\dmjt,2],  m       i  dp  Y*^^ 
\dm2/t,  V,  1 


It  will  be  observed  that  the  first  member  of  this  equation  relates 
solely  to  the  liquid  or  solid,  and  the  second  member  solely  to  the 
gas.  Now  we  may  suppose  the  same  gaseous  mass  to  be  capable  of 
equilibrium  with  several  diiferent  liquids  or  solids,  and  the  first  mem- 
ber of  this  equation  must  therefore  have  the  same  value  for  all  such 
liquids  or  solids  ;  which  is  quite  inadmissible.  In  the  simplest  case,  in 
which  the  liquid  or  solid  is  identical  in  substance  with  the  vapor 
which  it  yields,  it  is  evident  that  the  expression  in  question  denotes 
the  reciprocal  of  the  density  of  the  solid  or  liquid.  Hence,  when  a 
gas  is  in  equilibrium  with  one  of  its  components  both  in  the  solid 
and  liquid  states  (as  when  a  moist  gas  is  in  equilibrium  with  ice  and 
water),  it  would  be  necessary  that  the  solid  and  liquid  should  have 
the  same  density. 

The  foregoing  considerations  appear  sufiicient  to  justify  the  defini- 
tion of  an  ideal  gas-mixture  which  we  have  chosen.  It  is  of  course 
immaterial  whether  we  regard  the  definition  as  expressed  by  equation 
(273),  or  by  (279),  or  by  any  other  fundamental  equation  which  can 
be  derived  from  these. 

The  fundamental  equations  for  an  ideal  gas-mixture  corresponding 
to  (255),  (265),  and  (271)  may  easily  be  derived  from  these  equations 
by  using  inversely  the  substitutions  given  on  page  217.     They  are 

^,(c.  m,)  log  '-^^£^=r,-\.2,  {a,m,  log^-^,^J,  (291) 
=  V^^.{-.>n^^og^-^^-B,m,Y  (292) 

-  2^  {c,m,+a,  m,)  t  log  t  +^\  [ct,  m,  t  log  ^h^^^^).  (293) 

The  components  to  which  the  fundamental  equations  (273),  (279), 
(291)  (292),  293)  refer,  may  themselves  be  gas-mixtures.  We  may 
for  example  apply  the  fundamental  equations  of  a  binary  gas-mixture 


J.  W.  Gibbs — Eqidlihriut)i  of  Heterogeneous  Sultstuitces.      225 

to  a  mixture  of  hydrogen  and  air,  or  to  any  ternary  gas-mixture  in 
wliich  the  proportion  of  two  of  the  components  is  fixed.  In  fact,  tlie 
form  of  equation  (279)  which  applies  to  a  gas-mixture  of  any  pai'ticu- 
lar  number  of  components  may  easily  be  reduced,  when  the  propor 
tions  of  some  of  these  components  are  fixed,  to  the  form  whicli  ai)plies 
to  a  gas-mixture  of  a  smaller  niunber  of  components.  The  necessary 
substitutions  will  be  analogous  to  those  given  on  page  217.  But  the 
components  must  be  entirely  different  from  one  another  with  respect 
to  the  gases  of  which  they  are  formed  by  mixture.  We  cannot,  for 
example,  apply  equation  (279)  to  a  gas-mixture  in  which  the  com- 
ponents are  oxygen  and  air.  It  would  indeed  be  easy  to  form  a 
fundamental  equation  for  such  a  gas-mixture  with  reference  to  the 
designated  gases  as  components.  Such  an  equation  might  be  derived 
from  (279)  by  the  proper  substitutions.  But  the  result  would  be  an 
equation  of  more  complexity  than  (279).  A  chenncal  compound, 
however,  with  respect  to  Dalton's  law,  and  with  respect  to  all  the 
equations  which  have  been  given,  is  to  be  regarded  as  entirely  differ- 
ent from  its  components.  Thus,  a  mixture  of  hydrogen,  oxygen,  and 
vapor  of  water  is  to  be  regarded  as  a  ternary  gas-mixture,  having  the 
three  components  mentioned.  This  is  certainly  true  when  the  quanti- 
ties of  the  compound  gas  and  of  its  components  are  all  independently 
variable  in  the  gas-mixture,  without  change  of  temperature  or  pres- 
sure. Cases  in  which  these  quantities  are  not  thus  independently 
variable  will  be  considered  hereafter. 

Inferences  in  regard  to  Potentials  iti  Liquids  and  Solids. 

Such  equations  as  (264),  (268),  (276),  by  which  the  values  of 
potentials  in  pure  or  inixed  gases  may  be  derived  from  quantities 
capable  of  direct  measurement,  have  an  interest  which  is  not  confined 
to  the  theory  of  gases.  For  as  the  potentials  of  the  independently 
variable  components  which  are  common  to  coexistent  liquid  and  gas- 
eous masses  have  the  same  values  in  each,  these  expressions  will 
generally  afford  the  means  of  determining  for  liquids,  at  least  ap- 
proximately, the  potential  for  any  independently  variable  compon- 
ent Avhich  is  capable  of  existing  in  the  gaseous  state.  For  although 
every  state  of  a  liquid  is  not  such  as  can  exist  in  contact  with  a 
gaseous  mass,  it  will  always  be  possil)le,  when  any  of  the  components 
of  the  liquid  are  volatile,  to  bring  it  by  a  change  of  pressure 
alone,  its  temperature  and  composition  remaining  unchanged,  to 
a   state  for  which   there  is   a  coexistent  phase  of  vapor,   in   which 

Trans.  Conn.  Acad.,  Vol.  III.  29  May,  KSTfi. 


226       ./.  W.  Glbbs — EqulUbrium  of  Ileteroyeiieoits  Substances. 

the  values  of  the  potentials  of  the  volatile  components  of  the  liquid 
may  be  estimated  from  the  density  of  these  substances  in  the  vapor. 
The  variations  of  the  potentials  in  the  liquid  due  to  the  change  of 
pressure  will  in  general  be  quite  trifling  as  compared  with  the 
variations  which  are  connected  with  changes  of  temperature  or  ot 
composition,  and  may  moreover  be  readily  estimated  by  means  of 
equation  (272).  The  same  considerations  will  apply  to  volatile  solids 
with  respect  to  the  determination  of  the  potential  for  the  substance 
of  the  solid. 

As  an  application  of  this  method  of  determining  the  potentials 
in  liquids,  let  us  make  use  of  the  law  of  Henry  in  regard  to  the 
absorption  of  s^ases  by  liquids  to  determine  the  relation  between 
the  quantity  of  the  gas  contained  in  any  liquid  mass  audits  potential. 
Let  us  consider  the  liquid  as  in  equilibrium  with  the  gas,  and  let 
m'-^^  denote  the  quantity  of  the  gas  existing  as  such,  rn'-^^  the 
quantity  of  the  same  substance  contained  in  the  liquid  mass,  yUj  the 
potential  for  this  substance  common  to  the  gas  and  liquid,  v^^'>  and 
v^^^  the  volumes  of  the  gas  and  liquid.  When  the  absorbed  gas 
forms  but  a  very  small  part  of  the  liquid  mass,  we  have  by  Henry's 
law 

^  =  .4      J-,  (204) 

where  ^1  is  a  function  of  the  temperature  ;  and  by  (-'76) 


ni 


(G) 


;.,  =  i?+CMog-^^,  (295) 


v^ 


B  and  C  also  denoting  functions  of  the  tenq>erature.     Therefore 


m 


(L) 


It  will  be  seen  (if  we  disregai-d  the  difference  of  notation)  that  this 
equation  is  equivalent  in  form  to  (216),  which  was  deduced  from 
a  jorior*  considerations  as  a  probable  relation  between  the  quantity 
and  the  potential  of  a  small  component.  When  a  liquid  absoi'bs 
several  gases  at  once,  there  will  be  sevei'al  equations  of  the  form  of 
(296),  which  will  hold  true  simultaneously,  and  which  we  may  regard 
as  equivalent  to  equations  (217),  (218).  The  quantities  A  and  C  in 
(216),  with  the  corresponding  quantities  in  (21  7),  (218),  were  regarded 
as  functions  of  the  temperature  and  pressure,  but  since  the  potentials 
in  liquids  are  but  little  affected  by  the  pressure,  we  might  anticipate 
that  these  quantities  in  the  case  of  liquids  miglit  be  regarded  as  func- 
tions of  the  temperature  alone. 


J.  W.  Gihbs — EquUihrhDii  of  Ileteroqeneoun.  Substances.      227 

In  regard  to  equations  (216),  (2lV),  (218),  we  may  now  observe 
that  by  (264)  and  (276)  they  are  shown  to  hokl  true  in  ideal  gases  or 
gas-mixtures,  not  only  for  components  which  form  only  a  small  part 
of  the  whole  gas-mixture,  but  without  any  such  limitation,  and  not 
only  approximately  but  absolutely.  It  is  noticeable  that  in  this  case 
quantities  A  and  C  are  functions  of  the  temperature  alone,  and  do 
not  even  depend  upon  the  nature  of  the  gaseous  mass,  except  upon 
the  particular  component  to  which  they  relate.  As  all  gaseous  bodies 
are  generally  supposed  to  approximate  to  the  laws  of  ideal  gases  when 
sufficiently  rarefied,  we  may  regard  these  equations  as  approximately 
valid  for  gaseous  bodies  in  general  when  the  density  is  sufficiently 
small.  When  the  density  of  the  gaseous  mass  is  very  great,  but 
the  separate  density  of  the  comjionent  in  question  is  small,  the  equa- 
tions will  probably  hold  true,  but  the  values  of  A  and  C  may  not  be 
entirely  independent  of  the  pressure,  or  of  the  composition  of  the  mass 
in  respect  to  its  principal  components.  These  equations  will  also 
apply,  as  we  have  just  seen,  to  the  potentials  in  liquid  bodies  for  com- 
ponents of  which  the  density  iu  the  liquid  is  very  small,  whenever 
these  components  exist  also  in  the  gaseous  state,  and  conform  to  the 
law  of  Henry.  This  seems  to  indicate  that  the  law  expressed  by 
these  equations  has  a  very  general  application. 

Considerations  relating  to  the  Increase  of  Entropy  due  to  the 
Mixture  of  Gases  by  Diffusion. 
From  equation  (278)  we  may  easily  calculate  the  increase  of 
entropy  which  takes  place  when  two  different  gases  are  mixed  by 
diffusion,  at  a  constant  temperature  and  pressure.  Let  us  suppose 
that  the  quantities  of  the  gases  are  such  that  each  occupies  initially 
one  half  of  the  total  volume.     If  we  denote  this  volume  by  F,  the 

increase  of  entropy  will  be 

V  V 

m  ,  a^  log  F-f  mg  a^  log  F-  m^  a^  log  —  -  m^  a^  log  -^, 

or  {7n^  «,  +  >«2  ^'2)  log  2. 

p  F  -,  pV 

Now  m^a-^  =  ---,       and        m.^  a^  =  — y. 

Therefore  the  increase  of  entropy  may  be  represented  by  the  expres- 
sion 

^-  log  2.  (297) 

It  is  noticeable  that  the  value  of  this  expression  does  not  depend 
upon  the  kinds  of  gas  which  are  concerned,  if  the  quantities  are  such 
as  has  been  supposed,  except  that  the  gases  which  are  mixed  must  be 


228      ./  W.  Gihhs — Equilibrhim  of  Heterogeneous  Substances. 

of  different  kinds.  If  we  should  bring  into  contact  two  masses  of  the 
same  kind  of  gas,  they  would  also  mix,  but  there  would  be  no  in- 
crease of  entropy.  But  in  regard  to  the  relation  which  this  case 
bears  to  the  preceding,  we  must  bear  in  mind  the  following  considera- 
tions. When  we  say  that  when  two  different  gases  mix  by  diffusion, 
as  we  have  supposed,  the  energy  of  the  whole  remains  constant,  and 
the  entropy  receives  a  certain  increase,  we  mean  that  the  gases  could 
be  separated  and  brought  to  the  same  volume  and  temperature  which 
they  had  at  first  by  means  of  certain  changes  in  external  bodies,  for 
example,  by  the  passage  of  a  certain  amount  of  heat  from  a  warmer 
to  a  colder  body.  But  when  we  say  that  when  two  gas-masses  of  the 
same  kind  are  mixed  under  similar  circumstances  there  is  no  change 
of  energy  or  entropy,  we  do  not  mean  that  the  gases  which  have  been 
mixed  can  be  separated  without  change  to  external  bodies.  On  the 
contrary,  the  separation  of  the  gases  is  entirely  impossible.  We  call 
the  energy  and  entropy  of  the  gas-masses  when  mixed  the  same  as 
when  they  were  unmixed,  because  we  do  not  recognize  any  difference 
in  the  si\bstance  of  the  two  masses.  So  when  gases  of  different  kinds 
are  mixed,  if  we  ask  what  changes  in  external  bodies  are  necessary  to 
bring  the  system  to  its  original  state,  we  do  not  mean  a  state  in 
which  each  particle  shall  occupy  more  or  less  exactly  the  same  posi- 
tion as  at  some  previous  epoch,  but  only  a  state  which  shall  be 
undistinguishable  from  the  previous  one  in  its  sensible  properties. 
It  is  to  states  of  systems  thus  incompletely  defined  tliat  the  problems 
of  thermodynamics  relate. 

But  if  such  considerations  explain  why  the  mixture  of  gas-masses 
of  the  same  kind  stands  on  a  different  footing  from  the  mixture  of 
gas-masses  of  different  kinds,  the  fact  is  not  less  significant  that  the 
increase  of  entropy  due  to  the  mixture  of  gases  of  different  kinds,  in 
such  a  case  as  we  have  supposed,  is  indej^endent  of  the  nature  of  the 
gases. 

Now  we  may  without  violence  to  the  general  laws  of  gases  which 
are  embodied  in  our  equations  suppose  other  gases  to  exist  than  such 
as  actually  do  exist,  and  there  does  not  appear  to  be  any  limit  to  the 
resemblance  which  there  might  be  between  two  such  kinds  of  gas. 
But  the  increase  of  entropy  due  to  the  mixing  of  given  volumes  of 
the  gases  at  a  given  temperature  and  pressure  would  be  independent 
of  the  degree  of  similarity  or  dissimilarity  between  them.  We  might 
also  imaoine  the  case  of  two  gases  which  should  be  absolutely  identi- 
cal in  all  the  properties  (sensible  and  molecular)  which  come  into 
play  while  they  exist  as  gases  either  pure  or  mixed   with  each  other, 


J.  ^V.  Glbbs — Equllihriioti  of  Ileievogeneous  SuhsUtvces.      229 

but  which  sliouhl  differ  in  respect  to  the  attractions  between  tlieir 
atoms  antl  the  atoms  of  some  other  substances,  and  therefore  in  tlieir 
tendency  to  combine  Mith  such  sul)stances.  In  tlie  mixture  of  such 
gases  by  diffusion  an  increase  of  entropy  wouhl  take  ))hice,  although 
the  process  of  mixture,  dynamically  considered,  might  be  absolutely 
identical  in  its  minutest  details  (e\  en  with  i-espect  to  the  i)recise  path 
of  each  atom)  with  processes  which  might  take  ]>lace  without  any 
increase  of  entropy.  In  sucli  respects,  entropy  stands  strongly  con- 
trasted with  energy.  Again,  when  such  gases  have  been  mixed,  there 
is  no  more  irapossil)ility  of  the  separation  of  the  two  kinds  of  molecules 
in  virtue  of  their  ordinary  motions  in  the  gaseous  mass  without  any 
especial  external  influence,  than  there  is  of  the  separation  of  a  lumio- 
geneous  gas  into  the  same  two  parts  into  which  it  has  once  been 
divided,  after  tliese  have  once  been  mixed.  In  other  words,  the 
impossibility  of  an  uncompensated  decrease  of  entropy  seems  to  be 
reduced  to  improbability. 

There  is  perhaps  no  fact  in  tlie  molecular  theory  of  gases  so  well 
established  as  that  the  number  of  molecules  in  a  given  volume  at  a 
given  temperature  and  .pressure  is  the  same  for  every  kind  of  gas 
when  in   a  state  to  which  the  laws  of  ideal  gases  apply.     Hence  the 

quantity  — —  in  (297)  must  be  entirely  determined  by  the  number  of 

molecules  which  are  mixed.  And  the  increase  of  entropy  is  therefore 
determined  by  the  number  of  these  molecules  and  is  independent  of 
their  dynamical  condition  and  of  the  degree  of  difference  between 
them. 

The  result  is  of  the  same  nature  when  the  volumes  of  the  gases 
which  are  mixed  are  not  equal,  and  when  more  than  two  kinds  of  gas 
are  mixed.  If  we  denote  by  v^,  v^?  etc.,  the  initial  volumes  of  the 
different  kinds  of  gas,  and  by  V  as  before  the  total  volume,  the 
increase  of  entropy  may  be  written  in  the  form 

:E^  {m^  a^)  log  V-  :S^  {m,  a,  logy  J. 
And  if  we  denote  by  r,,  rg,  etc.,  the  numbers  of  the  molecules  of  the 
several  different  kinds  of  gas,  we  shall  have 

r^  =  (Jm^  «!,     ?'2  =  Cm^  a.^,    etc., 
where  (J  denotes  a  constant.     Hence 

V  ^:V::  m^a^ :  2  ^{m^a.^)  ::1\  :  ^,  r^ ; 
and  the  increase  of  entropy  may  be  written 

^^^ilog^i^i  -^i(^ilog^i)^  (298) 

C 


230      J.  W.  Gibbs — Equilibrhim  of  Heterogeneous  ^Substances. 

The  Phases  of  Dissipated  Energy  of  an   Ideal   Gas-ndxtare   loith 
Components  v^hivh  are  Vhemically  Related. 

We  will  now  pass  to  the  considevation  of  the  phases  of  dissipated 
energy  (see  page  200)  of  an  ideal  gas-mixture,  in  which  the  number 
of  the  proximate  components  exceeds  that  of  the  ultimate. 

Let  us  first  suppose  that  an  ideal  gas-mixture  has  for  proximate 
components  the  gases  6r,,  6^3,  and  6^g,  the  units  of  which  are 
denoted  by  @^,  @2,  @3,  and  that  in  ultimate  analysis 

@3  =  A,®,  +A2@2,  (299) 

A,  and  A2  denoting  positive  constants,  such  that  Aj  +  Ag  =  1.  The 
phases  which  we  are  to  consider  are  those  for  uiiich  the  energy  of 
the  gas-mixture  is  a  minimum  for  constant  entropy  and  volume  and 
constant  quantities  of  G^  and  6r g,  as  determined  in  ultimate  analysis. 
For  such  phases,  by  (86), 

/^i  8m  ^  4-  //g  6m.  ^  +  fx^  Sm^^O.  (300) 

for  such  values  of  the  variations  as  do  not  affect  the  quajitities  of 
(tj  and  6rg  as  determined  in  ultimate  analysis.  Values  of  dm^, 
6ino,  (Si)ip^  proportional  to  A,,  A,,  —  1,  and  only  such,  are  evidently 
consistent  with  this  restriction  :  therefore 

Aj  Ml  +  Ao  ^2  =  1^2-  (301) 

If  we  substitute  in  this  equation  values  of  fi^,  /^2?  /'a  taken  from 
(2*76),  we  obtain,  after  arranging  the  terms  and  dividing  by  t, 

^1  «i  log  V+  '^^  ""■'  ^""^  "V  ~  "'^  ^""^  "zT  ^  -^+  Slog^  — ?,  (302) 
where 

^  =  A,  JTj  +  Aa^o  — ^3-A,Cj-A2C2-f  Cg-Ajffj-Aatta  +  ^s^    (•'^03) 

^czrAjCj-fA^eo-Cg,  (304) 

G~\^E^-\-\„E^—  E^.  (305) 

If  we  denote  by  /^,  and  fi^  the  volumes  (determined  under  stand- 
ard conditions  of  temperature  and  pressure)  of  the  quantities  of 
the  gases  G  ^^  and  G^  which  are  contained  in  a  unit  of  volume  of  the 
gas  6^3,  we  shall  have 

/A  =  ^'\and   /i.  =  ^-|^,  (300) 


and  (302)  will  reduce  to  the  form 

log  "^^       T\  a ^  =  -   +  —  log  ^  -  — .  (307) 


^\nj'  A        B.  'C 


m„  V 


3       "3  "s 


J.  W.  Glbbs — J^fjiulibriuiti  of  Ileteroyeneous  ISubstaiices.      231 

Moreover,  as  by  (277) 

pv  =  {(fi  hi  ^  +  a.^  »*3  +  rtg  iii^)  f,  (;508) 

we  have  on  eliminating  v 

/:?,  ii.2      fi,    +  /3.^  —  1 

loff  ^1  '"2         P . 

»i3   («!  m,   -{-  «3  Wig    -f  «3   ?>?.3) 

^       ^'  C 

3  3  ^^  3   ^ 

where 

^'  ==  A  J   Cj  -f-  ^  2  <^2    -   *'3  +  '^  1  ^'  I    +   '^  2  ^i!    —   «3-  ("^  1  ") 

It  will  be  observed  that  the  quantities  /ij,  /J.^  will  always  be  posi- 
tive and  have  a  simple  relation  to  unity,  and  that  the  value  of 
/i,  -f  /!^2  ~  1  will  be  positive  or  zero,  according  as  gas  G^  is  formed 
of  (tj  and  G2  with  or  without  condensation.  If  we  should  assume, 
according  to  the  rule  often  given  for  the  specific  heat  of  compound 
gases,  that  the  thermal  capacity  at  constant  volume  of  any  quantity 
of  the  gas  6^3  is  equal  to  the  sum  of  the  thermal  capacities  of  the 
quantities  which  it  contains  of  the  gases  G^  and  G.^,  the  value  of  B 
would  be  zero.  The  heat  evolved  in  the  formation  of  a  miit  of  the  gas 
6^3  out  of  the  gases  G  ^  and  G2,  without  mechanical  action,  is  by 
(283)  and  (257) 

A ,  (c,  «  +  ^1)  +  A2  (c'2  t-^KJ  -  (C3  t+U^), 
or  Bt  -\-  a, 

which  will  reduce  to  C  when  the  above  relation  in  regard  to  the 
specific  heats  is  satisfied.  In  any  case  the  quantity  of  heat  thus 
evolved  divided  by  ^3  t^  will  be  equal  to  the  differential  coefficient  of 
the  second  member  of  equation  (307)  with  respect  to  t.  Moreover, 
the  heat  evolved  in  the  formation  of  a  unit  of  the  gas  G.^  out  of  the 
gases  6r,  and  G2  imder  constant  pressure  is 

Bt  +  C+A,«i  t  4-  A..a2t-a,,t=zB't-\-C, 
which  is  equal  to  the  differential  coefficient  of  the  second  member  of 
(309)  with  respect  to  t,  multiplied  by  a^  t'^ . 

It  appears  by  (307)  that,  except  in  the  case  when  ji ^  +  f-j^  =  1, 
for  any  given  finite  values  oi'  iii  ^,  in.,,  ni^,  and  t  (infinitesimal  values 
being  excluded  as  well  as  infinite),  it  will  always  be  possible  to 
assign  such  a  finite  value  to  v  that  the  mixture  shall  be  in  a  state  of 
dissipated  energy.  Thus,  if  Ave  regard  a  mixture  of  hydrogen,  oxy- 
gen, and  vapor  of  water  as  an  ideal  gas-mixture,  for  a  mixture  con- 
taining any  given  quantities  of  these  three  gases  at  any  given  tem- 


232      J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances. 

perature  there  will  be  a  certain  volume  at  which  the  mixture  will  be 
in  a  state  of  dissipated  energy.  In  such  a  state  no  such  phenomenon 
as  explosion  will  be  possible,  and  no  formation  of  water  by  the  action 
of  platinum.  (If  the  mass  should  be  expanded  beyond  this  volume, 
the  only  possible  action  of  a  catalytic  agent  would  be  to  resolve  the 
water  into  its  components.)  It  may  indeed  be  true  that  at  ordinary 
temperatures,  except  when  the  quantity  either  of  hydrogen  or  of 
oxygen  is  very  small  compared  with  the  quantity  of  water,  the  state 
of  dissipated  energy  is  one  of  such  extreme  rarefaction  as  to  lie 
entirely  beyond  our  power  of  experimental  verification.  It  is  also  to 
be  noticed  that  a  state  of  great  rarefaction  is  so  unfavorable  to  any 
condensation  of  the  gases,  that  it  is  quite  probable  that  the  catalytic 
action  of  platinum  may  cease  entirely  at  a  degree  of  rarefaction  far 
short  of  what  is  necessary  for  a  state  of  dissipated  energy.  But  with 
respect  to  the  theoretical  demonstration,  such  states  of  great  rarefac- 
tion are  precisely  those  to  which  we  should  suppose  that  the  laws  of 
ideal  gas-mixtures  would  apply  most  perfectly. 

But  when  the  compound  gas  G^  is  formed  of  6r,  and  G^  without 
condensation,  (i.  e.,  when  /i,  -\-  (i.^  =r  1,)  it  appears  from  equation  (307) 
that  the  relation  between  iit^,  m.^,  and  rn^  which  is  necessary  for  a 
phase  of  dissipated  energy  is  determined  by  the  temperature  alone. 

In  any  case,  if  we  regard  the  total  quantities  of  the  gases  G^  and 
6^2  (^s  determined  by  the  ultimate  analysis  of  the  gas-mixture),  and 
also  the  volume,  as  constant,  the  quantities  of  these  gases  which 
appear  uncombined  in  a  phase  of  dissipated  energy  will  increase  with 
the  temperature,  if  the  formation  of  the  compound  6^3  without 
change  of  volume  is  attended  with  evolution  of  heat.  Also,  if  we 
regard  the  total  quantities  of  the  gases  G^  and  G^,  and  also  the 
pressure,  as  constant,  the  quantities  of  these  gases  which  appear  un- 
combined in  a  phase  of  dissipated  energy,  will  increase  with  the 
temperature,  if  the  formation  of  the  compound  G^  under  constant 
pressure  is  attended  with  evolution  of  heat.  If  J5  =  0,  (a  case,  as 
has  been  seen,  of  especial  importance),  the  heat  obtained  by  the 
formation  of  a  unit  of  G^  out  of  G^  and  G2  without  change  of  volume 
or  of  temperature  will  be  equal  to  C.  If  this  quantity  is  positive, 
and  the  total  quantities  of  the  gases  G^  and  G2  and  also  the  volume 
have  given  finite  values,  for  an  infinitesimal  value  of  t  we  shall  have 
(for  a  phase  of  dissipated  energy)  an  infinitesimal  value  either  pf  m^ 
or  of  ^2,  and  for  an  infinite  value  of  t  we  shall  have  finite  (neither  in- 
finitesimal nor  infinite)  values  of  m,,  m^,  and  m^.  But  if  we  suppose 
the  pressure  instead  of  the  volume  to  have  a  given  finite  value   (with 


J.   W.  (ribbs — Eqiiilibriiim  of  Heterogeneous  ^<ubstances.      2;j3 

suppositions  otherwise  tlie  same),  we  shall  have  for  infinitesimal 
values  of  ^  an  infinitesimal  value  either  of  w/ ,  or  Wig,  and  for  infinite 
values  of  t  finite  or  infinitesimal  values  of  rit^  according  as  /j,  -|-  /i^ 
is  equal  to  or  greater  than  unity. 

The  case  which  we  have  considered  is  that  of  a  ternary  gas-mix- 
ture, but  our  results  may  easily  be  generalized  in  this  respect.  In 
fact,  whatever  the  number  of  component  gases  in  a  gas-mixture,  if 
there  are  relations  of  equivalence  in  ultimate  analysis  l)etween  these 
components,  such  relatioTis  may  be  expressed  by  one  or  more  equa- 
tions of  the  form 

A ,  (S^ ,   +  A2  C'^io  +  A  3  (SV^  +  etc.  in  0,  (31 1) 

where  @j,  (S^g?  ^^c.  denote  the  units  of  the  various  component  gases, 
and  A,,  A 2,  etc.  denote  positive  or  negative  constants  such  that 
2^  A ,  =:  0.  From  (311)  with  (R6)  we  may  derive  for  phases  of  dis- 
sipated energy, 

Aj   //j    +   A2  11-2   +  ^^3  /'3    +  ^tc.  =0, 

or  ^^j  (A,//,)  =  0.  (312) 

Hence,  by  (276), 

^,[^,a,\og~^)  =  A  +  B\o^t  ^  J,  (313) 

where  A,  B  and  ('  are  constants  determined  by  the  equations 

A  =  2,  {X,II,  -  A,c,  -  X,a,),  (314) 

B=^,{\,c,\  (315) 

C=2,{X,E,).  (316) 

Also,  since  2^  ^^  —  ^1  ('"'^  1  "'  1 )  ^ 

^' J  (A  ,  «j  log  «? , )  —  ^  (A  ^  a , )  log  JS"  J  (« J  m  , ) 

-f  ^^(A,«,)log/>  =  .4  +  ^'log<--^,  (317) 

where 

B'  =  2,  (A,c,-f  A,«J.  (318) 

If  there  is  more  than  one  equation  of  the  form  (311),  we  shall  have 
more  than  one  of  each  of  the  forms  (313)  and  (317),  which  will  hold 
true  simultaneously  for  phases  of  dissipated  energy. 

It  will  be  observed  that  the  relations  necessary  for  a  phase  of  dis- 
sipated energy  between  the  volume  and  temperature  of  an  ideal  gas- 
mixture,  and  the  quantities  of  the  components  which  take  part  in 
the  chemical  processes,  and  the  pressure  due  to  these  components,  are 
not  affected  by  the  presence  of  neutral  gases  in  the  gas-mixture. 

Trans.  Conn.  Acad.,  Vol.  III.  ::0  May,  187(3. 


'234     J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances. 

From  equations  (312)  and  (234)  it  follows  that  if  there  is  a  phase 
of  dissipated  energy  at  any  point  in  an  ideal  gas-mixture  in  equili- 
In-iuni  under  the  iutiuence  of  gravity,  the  whole  gas-mixture  must 
consist  of  such  phases. 

The  equations  of  the  phases  of  dissipated  energy  of  a  binary  gas- 
mixture,  the  components  of  which  are  identical  in  substance,  are  com- 
paratively simple  in  form.     In  this  case  the  two  components  have  the 

same  potential,  and  if  we  write  /i  for  —   (the  ratio  of  the  volumes  of 

equal  quantities  of  the  two  components  under  the  same  conditions  of 
temperature  and  pressure),  we  shall  have 

log ^ =  -^-  H log  t  -  — -,  (319) 

3—1       a,       cto  «2  ^ 

m^  V  d  ^  <£ 

log i-^^i —  — 1 lost-  — : ;     (-3^^) 

/  ,  V  /3— 1  «2  «P  «2   ^ 

where 

^  =  c,  -C2,  i?'  =  Ci  —  Cg  +«j  —  rtg,  (322) 

C=iE^~E^.  (323) 

Gas-mixtures  with  Convertible  Gom,ponents. 

The  equations  of  the  phases  of  dissipated  energy  of  ideal  gas-mix- 
tures which  have  components  of  which  some  are  identical  in  ultimate 
analysis  to  others  have  an  especial  interest  in  relation  to  the  theory 
of  gas-mixtures  in  which  the  components  are  not  only  thus  equivalent, 
but  are  actually  transformed  into  each  other  within  the  gas-mixture 
on  variations  of  temperature  and  pressure,  so  that  quantities  of  these 
(proximate)  components  are  entirely  determined,  at  least  in  any  per- 
manent phase  of  the  gas-mixture,  by  the  quantities  of  a  smaller 
number  of  ultimate  components,  with  the  temperature  and  pi-essure. 
Such  gas-inixtures  may  be  distinguished  as  having  convertible  com- 
ponents.  The  very  general  considerations  adduced  on  pages  197-203, 
which  are  not  limited  in  their  application  to  gaseous  bodies,  suggest 
the  hypothesis  that  the  equations  of  the  phases  of  dissipated  energy 
of  ideal  gas-mixtures  may  apply  to  such  gas-mixtures  as  have  been 
described.  It  will,  however,  be  desirable  to  consider  the  matter  more 
in  detail. 


J.  W.  (rlhhH — J^quilibriuin. of  Hetero(/en€OHS  Substances.      2'.\b 

In  the  first  place,  if  we  consider  tlic  case  of  a  gas-mixture  wliich 
only  diifers  from  an  ordinary  ideal  gas-mixture  for  which  some  of 
the  components  are  equivalent  in  that  there  is  perfect  freedom 
in  regard  to  the  ti'ansformation  of  these  components,  it  follows  at 
once  from  the  general  formula  of  equilibrium  (l)  or  (2)  that  equili- 
brium is  only  possible  for  such  phases  as  we  have  called  phases  of 
dissipated  energy,  for  which  some  of  the  characteristic  equations  have 
been  deduced  in  the  preceding  pages. 

If  it  should  be  urged,  that  regarding  a  gas-mixture  which  has 
convertible  components  as  an  ideal  gas-mixture  of  which,  for  some 
reason,  only  a  part  of  the  phases  are  actually  capable  of  existing,  we 
might  still  suppose  the  particular  phases  which  alone  can  exist  to  be 
determined  by  some  other  principle  than  that  of  the  free  convertibility 
of  the  components  (as  if,  perhaps,  the  case  were  analogous  to  one 
of  constraint  in  mechanics),  it  may  easily  be  shown  that  such  a  hypo- 
thesis is  entirely  untenable,  when  the  quantities  of  the  proximate 
components  may  be  varied  independently  by  suitable  variations  of  the 
temperature  and  pressure,  and  of  the  quantities  of  the  ultimate  com- 
ponents, and  it  is  admitted  that  'the  relations  between  the  energy, 
entropy,  volume,  temperature,  pi-essure,  and  the  quantities  of  the 
several  proximate  components  in  the  gas-mixture  are  the  same  as  for 
an  ordinary  ideal  gas-mixture,  in  which  the  components  are  not  con- 
vertible. Let  us  denote  the  quantities  of  the  n'  proximate  compo- 
nents of  a  gas-mixture  A  by  m^,  m^,  etc.,  and  the  quantities  of  its  n 
ultimate  components  by  nii,  nio,  etc.  {n  denoting  a  number  less  than 
w'),  and  let  us  suppose  that  for  this  gas-mixture  the  quantities  £,  ?/,  u, 
«, /J,  >«j,  ^2,  etc.  satisfy  the  relations  characteristic  of  an  ideal  gas- 
mixture,  while  the  phase  of  the  gas-mixture  is  entirely  determined  by 
the  values  of  m-i,  mg,  etc.,  with  two  of  the  quantities  f,  7,  w,  (?,/). 
We  may  evidently  imagine  such  an  ideal  gas-mixture  B  having  n' 
components  (not  convertible),  that  every  phase  of  A  shall  correspond 
yfMh  one  of  B  in  the  values  of  £,  7,  v,  t,  p,  m  j ,  mg ,  etc.  Now  let  us  give 
to  the  quantities  mj,  mg,  etc.  in  the  gas-mixture  A  any  fixed  values, 
and  for  the  body  thus  defined  let  us  imagine  the  v-7]-e  surfiice  (see 
page  1 74)  constructed  ;  likewise  for  the  ideal  gas-mixture  B  let  us 
imagine  the  v-i]-£  surface  constructed  for  every  set  of  values  of 
m^,  m^,  etc,  which  is  consistent  with  the  given  values  of  m^,  ixi^-, 
etc.  i.  e.,  for  every  body  of  which  the  ultimate  composition  would  be 
expressed  by  the  given  values  of  m , ,  mg ,  etc.  It  follows  immediately 
from  our  supposition,  that  every  point  in  the  v-f]-£  surface  relating  to 
A  must  coincide  with  some  point  of  one  of  the  v-if-e  surfaces  relating 


236      J.    W.  (J^ibbs — Equilibriuiii.  of  Ileterof/entous  Substances. 

to  £  not  only  in  respect  to  position  but  also  in  respect  to  its  tangent 
plane  (which  represents  temperature  and  pressure)  ;  therefore  the 
«-//-£  surface  relating  to  A  must  be  tangent  to  the  varioiis  v-r,-e  sur- 
faces relating  to  B,  and  therefore  must  be  ai]  envelop  of  these  sur- 
faces. P'roni  this  it  follows  that  the  points  which  represent  phases 
common  to  both  gas-mixtures  must  represent  the  phases  of  dissipated 
energy  of  the  gas-mixture  B. 

The  properties  of  an  ideal  gas-mixture  which  are  assumed  in 
regard  to  the  gas-mixture  of  converti1)le  components  in  the  above 
demonstration  are  expressed  by  equations  (277)  and  (278)  with  the 
equation 

e:=:£A'\>",f-^"'iE,).  (824) 

It  is  usual  to  assume  in  regard  to  gas-mixtures  liaving  convertible 
components  that  the  convertibility  of  the  components  does  not  affect 
the  relations  (277)  and  (324).  The  same  cannot  be  said  of  the  equa- 
tion (278).  But  in  a  very  important  class  of  cases  it  will  be  sufficient 
if  the  applicability  of  (277)  and  (324)  is  admitted.  The  cases  referred 
to  are  those  in  which  in  certain  phases  of  a  gas-mixture  the  compo- 
nents are  convertible,  and  in  other  phases  of  the  same  proximate 
composition  the  components  are  not  convertible,  and  the  equations  of 
an  ideal  gas-mixture  hold  true. 

If  there  is  only  a  single  degree  of  convertibility  between  the  com- 
ponents, (i.  e.,  if  only  a  single  kind  of  conversion,  with  its  reverse,  can 
take  place  among  the  components,)  it  Avill  be  sufficient  to  assume,  in 
regard  to  the  phases  in  which  conversion  takes  place,  the  validity  of 
equation  (277)  and  of  the  following,  which  can  be  derived  from  (324) 
by  differentiation,  and  comparison  with  equation  (11),  which  expresses 
a  necessary  relation, 

\t  d  )}  —p  dv  -  2j  (c^m^)  dt]  „.  =  0.*  (325) 

We  shall  confine  our  demonstration  to  this  case.  It  will  be  observed 
that  the  physical  signification  of  (325)  is  that  if  the  gas-mixture  is 
subjected  to  such  changes  of  volume  and  temperature  as  do  not  alter 
its  proximate  composition,  the  heat  absorbed  or  yielded  may  be  cal- 
culated by  the  same  formula  as  if  the  components  were  not  conver- 
tible. 

Let  us  suppose  the  thermodynamic  state  of  a  gaseous  mass  J/,  of 
such  a  kind  as  has  just  been  described,  to  be  varied  while  within  the 
limits  within  which  the  components  are  not  convertible.  (The  quan- 
tities of  the  proximate  components,  therefore,  as  well  as  of  the  ulti- 


*  This  notation  is  intended  to  indicate  that  ?;i|,  m.^,  etc.  are  regarded  as  constant 


J.   W' .  Glbbs — Kqa  11  lb  I'll  (III  of  Jleteroi/aneoiis  Sabst<incef<.       2;{7 

mate,  are  supposed  constant).  If  we  vise  the  same  metliod  of  geome- 
trical representation  as  before,  the  point  representing-  the  vohime, 
entropy,  and  energy  of  the  mass  will  describe  a  line  in  the  n-ij-f:  sur- 
face of  an  ideal  gas-mixture  of  inconvertible  components,  the  form 
and  position  of  this  surface  being  determined  by  the  proximate  comi)0- 
sition  of  31.  Let  us  now  suppose  the  same  mass  to  be  carried  beyond 
the  limit  of  inconvertibility,  the  variations  of  state  after  passino-  the 
limit  being  such  as  not  to  alter  its  proxinuxte  composition.  It  is 
evident  that  this  will  in  general  be  possible.  Exceptions  can  only 
occur  when  the  limit  is  formed  liy  phases  in  which  the  proximate 
composition  is  uniform.  The  line  traced  in  the  region  of  convertibility 
must  belong  to  the  same  »-?/-£  surface  of  an  ideal  gas-mixture  of  in- 
convertible components  as  before,  continued  beyond  the  limit  of 
inconvertibility  for  the  components  of  31,  since  the  variations  of 
volume,  entropy  and  energy  are  the  same  as  would  be  possible  if  the 
components  were  not  convertible.  But  it  must  also  belong  to  the 
v-7]-8  surface  of  the  body  J/,  which  is  here  a  gas-mixture  of  conver- 
tible components.  Moreover,  as  the  inclination  of  each  of  these 
surfaces  must  indicate  the  temperature  and  pressure  of  the  phases 
through  which  the  body  passes,  these  two  surfaces  must  be  tangent 
to  each  other  along  the  line  which  has  been  traced.  As  the  y-;/-£ 
surface  of  the  body  31  in  the  region  of  convertibility  must  thus  be 
tangent  to  all  the  surfaces  representing  ideal  gas-mixtiires  of  every 
possible  proximate  composition  consistent  with  the  ultimate  composi- 
tion of  31,  continued  beyond  the  region  of  inconvertibility,  in  which 
alone  their  form  and  position  may  be  capable  of  experimental  demon- 
stration, the  former  surface  must  be  an  envelop  of  the  latter  sui-faces, 
and  therefore  a  continuation  of  the  surface  of  the  phases  of  dissipated 
energy  in  the  region  of  inconvertibility. 

The  foregoing  considerations  may  give  a  measure  of  a  priori  prob- 
ability to  the  results  which  are  obtained  by  applying  the  ordinary 
laws  of  ideal  gas-mixtures  to  cases  in  which  the  components  are  con- 
vertible. It  is  only  by  experiments  upon  gases  in  phases  in  which 
their  components  are  convertible  that  the  validity  of  any  of  these 
results  can  be  established. 

The  very  accurate  determinations  of  density  which  have  been  made 
for  the  peroxide  of  nitrogen  enable  us  to  subject  some  of  our  equa- 
tions to  a  very  critical  test.  That  this  substance  in  the  gaseous  state 
is  properly  regarded  as  a  mixture  of  different  gases  can  hardly  be 
doubted,  as  the  proportion  of  the  components  derived  from  its  density 
on  the  supposition  that  one  component  has  the  molecular  formula 


238      tf.  W.  Gibbs — Equilihrintn  of  Heterogeneous  Substances. 

NOg  and  the  other  the  formula  N^O^  is  the  same  as  that  derived 
from  the  depth  of  the  color  on  the  supposition  that  the  absorption  of 
light  is  due  to  one  of  the  components  alone,  and  is  proportioned  to 
the  separate  density  of  that  component.* 

MM.  Sainte-Claire  Deville  and  Troostf  have  given  a  series  of  deter- 
minations of  what  we  shall  call  the  relative  densities  of  peroxide  of 
nitrogen  at  various  temperatures  under  atmospheric  pressure.  We 
use  the  terra  relative  density  to  denote  Avhat  it  is  usual  in  treatises  on 
chemistry  to  denote  by  the  term  density,  viz.,  the  actual  density  of  a 
gas  divided  by  the  density  of  a  standard  perfect  gas  at  the  same 
pressure  and  temperature,  the  standard  gas  being  air,  or  more  strictly, 
an  ideal  gas  which  has  the  same  density  as  air  at  the  zero  of  the 
centigrade  scale  and  the  pressure  of  one  atmos])here.  In  order  to 
test  our  equations  by  these  determinations,  it  will  be  convenient  to 
transform  equation  (320),  so  as  to  give  directly  the  relation  between 
the  relative  density,  the  pressure,  and  the  temperature. 

As  the  density  of  the  standard  gas  at  any  given  temperature  and 

P 

pressure  may  by  (263)  be  expressed   by  the  formula  -^—,  the  relative 

density  of  a  binary  gas-mixture  may  be  expressed  by 
Now  by  (263) 


a  t 
7>=  (m,  +^2)-^.  (326) 

^  ^   pv 


a^  7n^  -\-  ao  ni^  =:  — .  (327) 

By  giving  to   ^3    and  m^    successively  the  value  zero  in  these  equa- 
tions, we  obtain 

O  I  ^2 

where  D-^    and  Z>2    denote  the   values  of  D  when  the  gas  consists 
wholly  of  one  or  of  the  other  component.     If  we  assume  that 

JJ,=2IJ„  (329) 

we  shall  have 

From  (326)  we  have 


«i  =  2a2.  (330) 


m ,  -{-  n/^  :=.  JJ , 


*Salet,  "Sur  la  coloration  du  peroxyde  d'azote,"  Comptes  Eendiis,  vol.  Ixvii,  p.  488. 
f  Comptes  Rendus,  vol.  Ixiv,  p.  237. 


J.  TTT  a ihhs— Equilibrium  of  Heterogeneous  Substances.      239 
and  from  (327),  by  (828)  unci  (;i80), 


2  m,  -{-»i.,z=  I>J~-=i2J)-      , 


whence 


m,  =  (D,~lJ)i^-^,  (331) 

m,  =  2(7>-y>,)f3-  (•'^^2) 

By  (327),  (331),  and  (332)  we  obtain  from  (320) 

los^~ r.\      = log^ .  (333) 

^2  (Z>  -  i>i)  a,       a^        a„     °  «  ^       ' 

This  formula  will  be  more  convenient  for  purposes  of  calculation  if 
we  introduce  common  logarithms  (denoted  by  log,g)  instead  of 
hyperbolic,  the  temperature  of  the  ordinary  centigrade  scale  t,  instead 
of  the  absolute  temperature  t,  and  the  pressure  in  atmospheres  p„t 
instead  of  p  the  pressure  in  a  rational  system  of  units.  If  we  also 
add  the  logarithm  of  a,  to  both  sides  of  the  equation,  we  obtain 

•°g.» -^(i-S-x  =  ^  + 1 '"=■»  <'  +^"^"  -  ^3-  (^•^*) 

where  A  and  C  denote  constants,  the  values  of  which  are  closely  con- 
nected with  those  of  A  and  0. 

From  the  molecular  formula?  of  peroxide  of  nitrogen   NO^   and 
NgO^,  we  may  calculate  the  relative  densities 

14  +  32^^^^^  _  ^  .^      ^^^^^  j^    —  !^jhlf  ,0691  r=  3.178.    (335) 
1  2  '  -  2  ^        ' 

The  determinations  of  MM.   Deville  and   Troost  are  satisfactorily 
represented  by  the  equation 


iogio     2  (i>  -  1.589)  ^,+  273'  ^        ^ 


which  o'ives 


i)=  3.178+  (y  -  VW(3.178H-0) 


3118.6       , 
where  log  ^o^J=  9.47056  -  f_^^  -  logi  oP<u- 

In  the  first  part  of  the  following  table  are  given  in  successive  col- 
umns the  temperature  and  pressure  of  the  gas  in  the  several  experi- 
ments of  MM.  Deville  and  Troost,  the  relative  densities  calculated 
from  these  numbers  by  equation  (336),  the  relative  densities  as 
observed   and  the  difference  of  the  observed  and  calculated  relative 


240      ./  W.  Gihbs — Equilihrimn  of  Heterogeneous  S^ihstanees. 

densities.  It  will  be  observed  that  these  differences  are  quite  small, 
in  no  case  reaching  .03,  and  on  the  average  scarcely  exceeding  .01. 
The  significance  of  such  correspondence  in  favor  of  the  hypothesis  by 
means  of  which  equation  (336)  has  been  established  is  of  course 
diminished  by  the  fact  that  two  constants  in  the  equation  have  been 
determined  from  these  experiments.  If  the  same  equation  can  be 
shown  to  give  correctly  the  relative  densities  at  other  pressures  than 
that  for  Avhich  the  constants  have  been  determined,  such  correspon- 
dence will  be  much  more  decisive. 


t. 

Pat 

D 

calculated 
by  eq.  (336). 

D 

observed. 

diff. 

Observers. 

26.7 

2.676 

2.65 

-.026 

D. 

&  T. 

35.4 

2.524 

2,53 

+  .006 

D. 

&  T. 

39.8 

2.443 

2.46 

+  .017 

D. 

&  T. 

49.6 

2.256 

2.27 

+  .014 

D. 

&  T. 

60.2 

2.067 

2.08 

+  .013 

D. 

&  T. 

70.0 

1.920 

1.92 

.000 

D. 

&  T. 

80.6 

1.801 

1.80 

-.001 

D. 

&  T. 

90.0 

1.728 

1.72 

-.008 

D. 

&  T. 

100.1 

1.676 

1.68 

+  .004 

D. 

&  T. 

111.3 

1.641 

1.65 

+  .009 

D. 

&  T. 

121.5 

1.622 

1.62 

-.002 

D. 

&  T. 

135.0 

1.607 

1.60 

-.007 

D. 

&  T. 

154.0 

1.597 

1.58 

-.017 

D. 

&  T. 

183.2 

1.592 

1.57 

-.022 

D. 

&  T. 

97.5 

1.687 

97.5 

iHf? 

1.631 

1.783 

+  .152 

P. 

&  W. 

24.5 

2.711 

24.5 

\nn 

2.524 

2.52 

-.004 

P. 

&  W. 

11.3 

2.891 

11.3 

'442  6  5 

2.620 

2.645 

+  .025 

P. 

&  w. 

4.2 

2.964 

4.2 

3  S  4  3  8 

2.708 

2.588 

-.120 

P. 

&  w. 

Messrs.  Playfair  and  Wanklyn  have  published*  four  determinations 
of  the  relative  density  of  peroxide  of  nitrogen  at  various  temperatures 
when"diluted  with  nitrogen.  Since  the  relations  expressed  by  equa- 
tions (319)  and  (320)  are  not  affected  by  the  presence  of  a  third  gas 
which  is  different  from  the  gases  O^  and  G2  (to  which  m.^  and  ui^ 
relate)  and  neutral  to  them,  (see  the  remark  at  the  foot  of  page  233), 
— provided  that  we  take^j)  to  denote  the  pressure  which  we  attribute  to 
the  gases  (x,  and  (t2i^-  ^-i  the  total  pressure  diminished  by  the  pressui-e 
which  the  third  gas  would  exert  if  occupying  alone  the  same  space  at 
the  same  temperature, — it  follows  that  the  relations  expressed  for 

*  Transactions  of  the  Royal  Society  of  Edinburg,  vol.  xxii,  p.  441. 


./  W.  Gihhs — EqxIJlhrhoii.  of  Heterogeneous  Suhstancex.      241 

peroxide  of  nitrogen  by  (333),  (334),  and  (336)  will  not  be  aliected 
by  the  presence  of  free  nitrogen,  if  the  pressure  expressed  bv  ^>  or 
jt),„  and  contained  implicitly  in  the  symbol  IJ  (see  equation  (320)  l)y 
which  D  is  defined)  is  understood  to  denote  the  total  pressure  dimin- 
ished by  the  pressure  due  to  the  free  nitrogen.  The  determinations 
of  Playfiiir  and  Wanklyn  are  given  in  the  latter  part  of  the 
above  table.  The  pressures  given  are  those  obtained  by  subtracting 
the  pressure  due  to  the  free  nitrogen  from  the  total  pi-essure.  We 
may  suppose  such  reduced  pressures  to  have  been  used  in  the  reduction 
of  the  observations  by  which  the  numbers  in  the  column  of  observed 
relative  densities  were  obtained.  Besides  the  relative  densities 
calculated  by  equation  (336)  for  the  temperatures  and  (reduced) 
pressures  of  the  observations,  the  table  contains  the  relative  densities 
calculated  for  the  same  tem])eratures  and  the  pressure  of  one  atmos- 
phere. 

The  reader  will  observe  that  in  the  second  and  third  experiments 
of  Playfair  and  Wanklyn  there  is  a  very  close  accordance  between 
the  calculated  and  observed  values  of  D,  while  in  the  second 
and  fourth  experiments  there  is  a  considerable  diiference.  Now  the 
weight  to  be  attributed  to  the  several  determinations  is  very  diifer- 
ent.  The  quantities  of  peroxide  of  nitrogen  which  were  used  in  the 
several  experiments  were  respectively  .2410,  .5893,  .3166,  and  .2016 
grammes.  For  a  rough  approximation,  Ave  may  assume  that  the 
probable  errors  of  the  relative  densities  are  inversely  proportional  to 
these  numbers.  This  would  make  the  probable  error  of  the  first  and 
fourth  observations  two  or  three  times  as  great  as  that  of  the  second 
and  considerably  greater  than  that  of  the  third.  We  must  also 
observe  that  in  the  first  of  these  experiments,  the  observed  relative 
density  1.783  is  greater  than  1.687,  the  relative  density  calculated  by 
equation  (336)  for  the  temperature  of  the  experiment  and  the  pres- 
sure of  one  atmosphere.  Now  the  number  1.687  we  may  regard  as 
established  directly  by  the  experiments  of  Deville  and  Troost. 
For  in  seven  successive  experiments  in  this  part  of  the  series  the 
calculated  relative  densities  difter  from  the  observed  by  less  than  .01. 
If  then  we  accept  the  numbers  given  by  experiment,  the  efiect  of 
diluting  the  gas  with  nitrogen  is  to  increase  its  relative  density.  As 
this  result  is  entirely  at  variance  with  the  facts  observed  in  the  case 
of  other  gases,  and  in  the  case  of  this  gas  at  lower  temperatures, 
as  appears  from  the  three  other  determinations  of  Playfair  and 
Wanklyn,  it  cannot  possibly  be  admitted  on  the  strength  of  a  single 
Trans.  Conn.  Acad.,  Vol.  III.  31  Mat,  187r,. 


242      J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances. 

observation.  The  first  experiment  of  this  series  cannot  therefore 
properly  be  used  as  a  test  of  our  equations.  Similar  considerations 
apply  with  somewhat  less  force  to  the  last  experiment.  By  compar- 
ing the  temperatures  and  pressures  of  the  three  last  experiments 
with  the  observed  relative  densities,  the  reader  may  easily  convince 
himself  that  if  we  admit  the  substantial  accuracy  of  the  determina- 
tions in  the  two  first  of  these  experiments  (the  second  and  third  of 
the  series,  which  have  the  greatest  weight),  the  last  determination  of 
relative  density  2.588  must  be  too  small.  In  fact,  it  should  evidently 
be  greater  than  the  number  in  the  preceditig  experiment  2.645. 

If  we  confine  our  attention  to  the  second  and  third  expei'iments  of 
the  series,  the  agreement  is  as  good  as  could  be  desired.  Nor  will 
the  admission  of  errors  of  .152  and  .120  (certainly  not  large  in  deter- 
minations of  this  kind)  in  the  first  and  fourth  experiments  involve 
any  serious  doubt  of  the  substantial  accuracy  of  the  second  and  third, 
when  the  difference  of  weight  of  the  determinations  is  considered. 
Yet  it  is  much  to  be  desired  that  the  relation  expressed  by  (336),  or 
with  more  generality  by  (334),  should  be  tested  by  more  numerous 
experiments. 

It  should  be  stated  that  the  numbers  in  the  column  of  pressures  are 
not  quite  accurate.  In  the  experiments  of  Deville  and  Troost 
the  gas  was  subject  to  the  actual  atmospheric  pressure  at  the  time  of 
the  experiment.  This  A^aried  from  747  to  764  millimeters  of  mercury. 
The  precise  pressure  for  each  experiment  is  not  given.  In  the  ex- 
periments of  Playfair  and  Wanklyn  the  mixture  of  nitrogen  and 
peroxide  of  nitrogen  was  subject  to  the  actual  atmospheric  pressure 
at  the  time  of  the  experiment.  The  numbers  in  the  column  of  pres- 
sures express  the  fraction  of  the  whole  pressure  wliich  remains  after 
substracting  the  part  due  to  the  free  nitrogen.  But  no  indication  is 
given  in  the  published  account  of  the  experiinents  in  regard  to  the 
height  of  the  barometer.  Now  it  may  easily  be  shown  that  a  varia- 
tion of  j^^xs  ill  t.he  value  of  p  can  in  no  case  cause  a  variation  of  more 
than  .005  in  the  value  of  D  as  calculated  by  equation  (336).  In  any 
of  the  experiments  of  Playfair  and  Wanklyn  a  variation  of  more 
than  30"""  in  the  height  of  the  barometer  would  be  necessary  to 
produce  a  variation  of  .01  in  the  value  of  D.  The  errors  due  to  this 
source  cannot  therefore  be  very  serious.  They  might  have  been 
avoided  altogether  in  the  discussion  of  the  experiments  of  Deville 
and  Troost  by  using  instead  of  (336)  a  formula  expressing  the 
relation  between  the  relative  density,  the  temperature,  and  the  actual 
density,  as  the  reciprocal  of  the  latter  quantity  is  given  for  each  ex- 


J.  W.  (rlhbs — I'JquUlbrluiii  of  Heterogeneous  Substances.      24.3 

perimeiit  of  this  series.  It  seemed  best,  however,  to  make  a  triHiiio; 
sacrifice  of  accxiracy  for  the  sake  of  simplicity. 

It  might  be  thought  that  the  experiments  under  discussion  would 
be  better  represented  by  a  formula  in  which  the  term  containing  log  t 
(see  equation  (333))  was  retained.  But  an  examination  of  the  figures 
in  the  table  will  show  that  nothing  important  can  be  gained  in  this 
respect,  and  there  is  hardly  sufticient  motive  for  adding  another  term 
to  the  formula  of  calculation.  Any  attempt  to  determine  the  real 
values  of  A,  B',  and  C  in  equation  (333),  (assuming  the  absolute 
validity  of  such  an  equation  for  peroxide  of  nitrogen,)  from  the  ex- 
periments under  discussion  would  be  entirely  misleading,  as  the 
reader  may  easily  convince  himself. 

From  equation  (336),  however,  the  following  conclusions  may 
deduced.     By  comparison  with  (334)  we  obtain 

.    ,  ^'                     C             ^             311S.6 
A  +  —  log.o  «  -  7  =  9-47056 ^, 

which  must  hold  true  approximately  between  the  temperatures  11*^ 
and  90'\  (At  higher  temperatures  the  relative  densities  vary  too 
slowly  Avith  the  temperatures  to  afibrd  a  critical  test  of  the  accuracy 
of  this  relation.)     By  diiFerentiation  we  obtain 

Jlf_S'C_  3118.6 

a^t    *"  ¥~       W~' 

where  31  denotes  the  modulus  of  the  common  system  of  logarithms. 

Now  by  comparing  equations  (333)  and  (334)  we  see  that 

MC  C 

C  = =  .43429  — . 

Hence 

B'i-^  C=  7181  «2  =  3590  «j, 

which  may  be  regarded  as  a  close  approximation  at  40'-'  or  50^',  and 
a  tolerable  approximation  between  the  limits  of  temperature  above 
mentioned.  Now  B'  t  +  C  represents  the  heat  evolved  by  the  con- 
version of  a  unit  of  NOg  into  NgO^  under  constant  pressure.  Such 
conversion  cannot  take  place  at  constant  pressure  without  change  of 
temperature,  which  renders  the  experimental  verification  of  the  last 
equation  less  simple.  But  since  by  equations  (322) 
B'  =  B+a^  -  rt2  =  ^  +  i«i, 
we  shall  have  for  the  temperature  of  40*^' 

Bt-\-  C;=3434a,. 
Now  B  t  -\-  (J  reiH-esents  the  decrease  of  energy  when  a  unit  of  NOg  is 
transformed  into  NgO^  without  change  of  temperature.     It  therefore 


244      J.  W.  Gihbs — EquUihrium  of  Heterogeneous  Substances. 

represents  the  excess  of  the  heat   evolved  over  the  work   done  by 

external  forces  when   a  mass  of  the  gas  is  compressed  at  constant 

temperatnre  until  a  unit  of  NO 3   has   been  converted  into   NgO^. 

This  quantity  will  be  constant  if  J3  =zO,  i.  e.,  if  the  specific  heats  at 

constant  volume  of  NO^  and  N2O4   ^i"e  the  same.     This  assumption 

would  be  more   simple  from   a  theoretical   stand-jjoint   and  perhaps 

safer  than  the  assumption  that  B'  =  0.     li  B  =1  0,  B'  =  a^.     If  we 

wish  to  embody  this  assumption  in  the  equation  between  Z>,  p^  and  t, 

we  may  substitute 

2977  4 
6.5228  +  log,  „  {t,  +  273)  ^  j^i^^ 

for  the  second  member  of  equation  (336).  The  relative  densities 
calculated  by  the  equation  thus  modified  from  the  temperatures  and 
pressures  of  the  experiments  under  discussion  will  not  diflTer  from 
those  calculated  from  the  unmodified  equation  by  more  than  .002  in 
any  case,  or  by  more  than  ,001  in  the  first  series  of  experiments. 

It  is  to  be  noticed  that  if  we  admit  the  validity  of  the  volumetrical 
relation  expressed  by  equation  (333),  which  is  evidently  equivalent 
to  an  equation  between  p,  t,  y,  and  ni  (this  letter  denoting  the  quan- 
tity of  the  gas  without  reference  to  its  molecular  condition),  or  if  we 
admit  the  validity  of  the  equation  only  between  certain  limits  of 
temperature  and  for  densities  less  than  a  certain  limit  of  density,  and 
also  admit  that  between  the  given  limits  of  temperature  the  specific 
heat  of  the  gas  at  constant  volume  may  be  regarded  as  a  constant 
quantity  when  the  gas  is  sufficiently  rarefied  to  be  regarded  as  con- 
sisting wholly  of  NO2, — or,  to  speak  without  reference  to  the  m.olecu- 
lar  state  of  the  gas,  when  it  is  rarefied  until  its  relative  density  D 
approximates  to  its  limiting  value  Z>,, — we  must  also  admit  the 
validity  (within  the  same  limits  of  temperature  and  density)  of  all  the 
calorimetrical  relations  which  belong  to  ideal  gas-mixtures  with 
convertible  components.  The  premises  are  evidently  equivalent  to 
this, — that  we  may  imagine  an  ideal  gas  with  convertible  components 
such  that  between  certain  limits  of  temperature  and  above  a  certain 
limit  of  density  the  relation  between  p,  t,  and  v  shall  be  the  same  for 
a  unit  of  this  ideal  gas  as  for  a  unit  of  peroxide  of  nitrogen,  and  for 
a  very  ^reat  value  of  0  (witliin  the  given  limits  of  temperature)  the 
thermal  capacity  at  constant  volume  of  the  ideal  and  actual  gases 
shall  be  the  same.  Let  us  regard  t  and  v  as  independent  variables ; 
we  may  let  these  letters  and  p  refer  alike  to  the  ideal  and  real  gases, 
but  we  must  distinguish  the  entropy  ?/'  of  the  ideal  gas  from  the 
entropy  tf  of  the  real  gas.     Now  by  (88) 


J.  W.  Gibbs — Equilibrimn  of  Heterogeneous  Substances.      245 
dn        dp 
therefore 


d    dt] 

d    dfj        d    dp        d~p 

dv     dt   ~ 

dt    dv  ~  dt    dt  ~   dt^' 

(338) 

Since  a  similar  relation  will  hold  true  for  //,  we  obtain 

d     dy]  d     dtf 

d^    ~dt~d^    ~dV  (^'^^^ 

which  must  hold  true  within  the  given  limits  of  temperature  and 
density.     Now  it  is  granted  that 

dt  -   dt  ^^^^^ 

for  very  great  values  of  o  at  any  temperature  Avithin  the  given  limits, 
(for  the  two  members  of  the  equation  represent  the  thermal  capacities 
at  constant  volume  of  the  real  and  ideal  gases  divided  by  ^,)  hence, 
in  virtue  of  (339),  this  equation  must  hold  true  in  general  within  the 
given  limits  of  temperature  and  density.  Again,  as  an  equation  like 
(337)  will  hold  true  of  ?/',  we  shall  have 

drj  dii 

dv        dv'  ^       ' 

From  the  two  last  equations  it  is  evident  that  in  all  calorimetrical 
relations  the  ideal  and  real  gases  are  identical.  Moreover  the  energy 
and  entropy  of  the  ideal  gas  are  evidently  so  far  arbitrary  that  we 
may  suppose  them  to  have  the  same  values  as  in  the  real  gas  for  any 
given  values  of  t  and  v.  Hence  the  entropies  of  the  two  gases  are 
the  same  within  the  given  limits  ;  and  on  account  of  the  necessary 
relation 

ds-=.  t  dt]  —  p  dv, 

the  energies  of  the  two  gases  are  in  like  manner  identical.  Hence 
the  fundamental  equation  between  the  energy,  entropy,  volume,  and 
quantity  of  matter  must  be  the  same  for  the  ideal  gas  as  for  the 
actual. 

We  may  easily  form  a  fundamental  equation  for  an  ideal  gas-mix- 
ture with  convertible  components,  which  shall  relate  only  to  the 
phases  of  equilibrium.  For  this  purpose,  we  may  use  the  e(piations 
of  the  form  (312)  to  eliminate  from  the  equation  of  the  form  (273), 
which  expresses  the  relation '  between  the  pressure,  the  temperature, 
and  the  potentials  for  the  proximate  components,  as  many  of  the 
potentials  as  there   are  equations  of  the  former  kind,  leaving  the 


246       J.  W.  Gibbs — Equilibrium  of  Heterogeneous  Substances. 

potentials  for  those  components  which  it  is  convenient  to  regard  as 
the  ultimate  components  of  the  gas-mixture. 

In  the  case  of  a  binary  gas-mixture  with  convertible  components, 
the  components  will  have  the  same  potential,  which  may  be  denoted 
by  //,  and  the  fundamental  equation  will  be 

Ci+ a,    //  —  -£/,  c.2-i-a.2    /U  —  E2 

p  =  a^L^t  e  -\-a.^L^t  e     ^    ,  (342) 

where 


(343) 

From  this  equation,  by  differentiation  and  comparison 

with 

(98),  we 

obtain 

c,    ii-E, 
-=^c,  +  a,-~--jt     e 

+  -^2  ( <'2  +  «2  -^ ~t U'e           , 

(244) 

c^    jLi  —  Ef                c-i     fi — E2 
-  =  L^t     e          -{-  L^t     e 

(345) 

From  the  'general  equation  (93)  with  the  preceding  eqiiations  the 
following  is  easily  obtained, — 

c^    [i—E^  Cj^    li  —  Ej 

--L^{c^t^E^)t""  e  "'^     ■^L^{c^t^E.^)f'  e  "-'^  .      (346) 

We  may  obtain  the  relation  between  jo,  t,  v,  and  ni  by  eliminating 
pi  from  (342)  and  (345).  For  this  purpose  we  may  proceed  as  follows- 
From  (342)  and  (345)  we  obtain 

Cj  -t-a,     fJ-—Ei 

Cj  +  Ct2     /^  — -5*2 

a^t p  —  (a^  -  Uo)  E^t       '     e     '     ;  (348) 

and  from  these  equations  we  obtain 

a,  log  Ip-a^t^-^j-a^log  ia,t"^-p]  =  {a^  -  "3)  log  (a,— aj 

E  —  7^ 

+  a,logii-«2log^-'3+(^'2-''2+^«i-«2)log« --r-^'     (349) 


J.  IK  Gihha — Equilibrium  of  TTelerogeneous  Substances.     247 

(In  the  particular  case  when  a,  =  2  «„  tliis  equation  will  he  e(iuiva- 
lent  to  (333)).  By  (347)  and  (348)  we  may  easily  eliminate  i^i  from 
(346). 

The  reader  will  observe  that  the  relations  thus  deduced  from  the 
fundamental  equation  (342)  without  any  reference  to  the  different 
components  of  the  gaseous  mass  are  equivalent  to  those  which  relate 
to  the  phases  of  dissipated  energy  of  a  binary  gas-mixture  with  com- 
ponents which  are  equivalent  in  substance  but  not  convertible,  except 
that  the  equations  derived  from  (342)  do  not  give  the  quantities  of 
the  proximate  components,  but  relate  solely  to  those  properties  which 
are  capable  of  direct  experimental  verification  without  the  aid  of  any 
theory  of  the  constitution  of  the  gaseous  mass. 

The  practical  apj^lication  of  these  equations  is  rendered  more  simple 
by  the  fact  that  the  ratio  a^'.a^  will  always  bear  a  simple  relation  to 
unity.  When  a,  and  «2  are  equal,  if  we  write  a  for  their  common 
value,  we  shall  have  by  (342)  and  (345) 

2?  V  =1  a  m  t,  (3.50) 

and  by  (345)  and  (346) 


m  C2~C|  E.  —E2 

at 


(.351) 


ij  -j-  2^2^  ^ 

By  this  equation  we  may  calculate  directly  the  amount  of  heat 
required  to  raise  a  given  quantity  of  the  gas  from  one  given  tempera- 
ture to  another  at  constant  volume.  The  equation  shows  that  the 
amount  of  heat  will  be  independent  of  the  volume  of  the  gas.  The 
heat  necessary  to  produce  a  given  change  of  temperature  in  the  gas 
at  constant  pressure,  may  be  found  by  taking  the  difference  of  the 
values  of  J,  as  defined  by  equation  (89),  for  the  initial  and  final  states 
of  the  gas.     From  (89),  (350),  and  (351)  we  obtain 

Cj—Cj,   El— Est 
Z  _  Z^{cit-\-at+B^)  +  L2{c2t  +  at+E^)t    ""    e     "^     ^   .g^^) 

L^+L„t         e 
By  differentiation  of  the  two  last   equations  we  may  obtain  directly 
the  specific  heats  of  the  gas  at  constant  volume  and  at  constant  pres- 
sure. 

The  fundamental  equation  of  an  ideal  ternary  gas-mixture  with  a 
single  relation  of  convertibility  between  its  components  is 


248      J.  JV.  Gibbs — Equilibrium  of  Heterogeneous  Substances. 

Hi—Ci  —  a^    c, +a|    n^—E^ 

a,  ,     a,  ttjt 

p  =  a^  e  t  e 

a.,  ^     O'i  o,>t 

4-  r/g  e  '        t  e 

+  «3  e  t      ^     e  ,  (353) 

where  Aj  and  X.^  have  the  same  meaning  as  on  page  230. 

{I'o  he  continued.) 


ERRATA. 
Page  167,  formula  (168),  for  m,  read  fi^. 

"        formula  (169),  for  to,,  .  .  .  m„_j  read/z,,  .  .  .  //«— i- 

Page  239.  formula  (333),  for—  read  _iL. 

t  ttat 


VI.  The  Hydroids  op  the  Pacific  Coast  of  the  United  States, 
SOUTH  OF  Vancouver  Island.  With  a  Report  upon  those 
IN  THE  Museum  of  Yale  College.     Bv  S.  F.  Clari 


Read  Jan.  19.  18  T  6. 


The  Museum  is  indebted  for  its  collection  of  Californian  Hydroids 
chiefly  to  Pro!'.  D.  C.  Eaton,  who  has  presented  during  the  last  two  or 
three  years,  a  large  number  of  specimens,  that  were  received  by  him 
with  dried  algtt?  from  that  coast.  They  were  collected  and  sent  to 
him  by  Dr.  C.  W.  Anderson,  Santa  Cruz,  Cal. ;  Dr.  L.  N.  Dimmick, 
Santa  Barbara,  Cal. ;  Mi-s.  Ell  wood  Cooper,  Santa  Barbara,  Cal.  ; 
and  ^Nliss  jNIitchell  of  Vancouver  Island.  All  the  specimens  received 
from  these  sources  were  collected  in  tide-pools  along  the  shore  or 
attached  to  algae,  washed  in  froui  deeper  water.  A  few  alcoholic 
specimens  have  also  been  received  from  San  Diego,  Cal.,  collected  on 
the  piles  of  the  Avharves  and  along  the  shore,  by  Dr.  E.  Palmer,  and 
a  fine  specimen  of  Plumularia  setacea  was  dredged  in  six  to  eight 
fathoms,  oil'  San  Diego,  by  Mr.  Henry  Hemphill. 

Some  of  the  species,  including  most  of  the  Sertnlarid(e,  do  not 
seem  to  be  injured  by  being  dried,  but  others,  as  the  Campannlaridce, 
ai'e  usually  rendered  useless  for  description.  The  specimens  of  the 
two  species  of  < ■ampanularia  described  below  are  unusually  well 
preserved,  both  hydrothecae  and  gonothecae  being  in  good  condition. 

There  has  been  very  little  published  on  the  hydroids  of  the 
western  coast  of  North  America,  up  to  tlie  present  time.  In  1857 
Dr.  Trask*  described  and  figured  nine  new  species  of  Zoophytes 
from  the  Bay  of  San  Francisco  and  adjacent  localities.  Five  of 
these  are  Bryozoa ;  the  remaining  four  represent  three  genera  of  the 
family  Sertularidie,  as  follows:  Sertularia  anguind,  S./ureata,  Sertu- 
lareUa  turgida  and  HydvaUmania  Franciscana,  all  of  which,  so  far 
as  I  am  aware,  are  peculiar  to  that  coast ;  unless  indeed  the  last 
named    species    prove   to  be  identical  with  H.  falcata  of  Europe, 


*  Proceedings  of  the  California  Academy  of  Natural  Sciences,  vol.  i,  March,  1357. 
Dr.  J.  B.  Trask. 
Trans.  Conn.  Acad.,  Vol.  III.  1  June,  1876. 


250  S.  M  Clarh — Hydroids  of  the  Pacific  Coast. 

Africa  and  New  England.  In  1860  Andrew  Murray*  described  and 
figured  five  species  from  the  Californian  coast,  of  which  three  are 
new,  and  the  other  two,  Sertidaria  labrata  and  Plumalaria  gracilis^ 
are  synonymous  with  two  of  Trask's  species,  viz  :  Sertularia  anguina 
and  Plumularia  Franciscana.  Mr.  Alexander  Agassizf  in  1865 
described  seven  species  and  recorded  seven  others  from  the  Bay  of 
San  Francisco  ;  and  he  had  three  of  the  same  from  the  Gulf  of  Georgia, 
W.  T.  Five  species  were  also  mentioned  by  him  from  the  North 
Pacific.  Two  of  these  five  northern  species,  Bougainvillia  Mertensii 
Ag.  and  Cotidina  Greenei  A.  Ag.,  are  also  found  at  San  Francisco. 
The  latter  species  having  also  been  collected  at  Santa  Barbara, 
Cal.,  has  the  wide  j-ange  of  nearly  three  thousand  miles  upon  our 
western  coast.  Professor  Allman  mentions  having  found  sixteen 
species  in  a  collection  from  the  Californian  coast,  siil)mitted  to  him 
for  examination  ;  two  of  them,  Lafoea.  dumosa  and  Sertularia  pumila, 
are  common  on  the  European  and  New  England  coasts,  and  the  former 
species  is  also  recorded  from  South  Africa.  The  collection  in  the 
Museum  of  Yale  College  contains  twelve  species  and  one  variety.  Of 
these  four  are  new ;  nine  are  recorded  only  from  the  Pacific  coast  of 
North  America,  as  yet;  and  three,  Halecium.  tenellum^  ISertularia 
argentea  and  Phmiidaria  setacea,  are  also  common  on  the  European 
shores;  the  first  two  of  these  have  also  been  found  on  the  New  England 
coast,  from  Maine  to  Long  Island  Sound.  The  most  common  form  on 
the  Californian  coast  is  the  showy  Aglaophenia  struthionides,  which  is 
apparently  as  abundant  there  as  Sertularia  argentea  and  S.  pumila  are 
upon  our  eastern  shores,  for  it  forms  the  bulk  of  every  package  sent 
to  lis  from  the  western  coast.  The  folloAving  table  gives  a  list  of  all 
the  Hydroids  known  on  the  western  coast  of  the  United  States,  from 
Vancouver's  Island  to  San  Diego,  with  the  range  of  tlie  different 
species  and  the  names  of  some  of  the  collectors. 

List  of  Hydroida  known  to  occur  between  San  Diego  and  Vancouver 

Island. 

Coryne  rosaria  A.  Ag.  Bay  of  San  Francisco,  Cal.  (A.  Agassiz). 

Tubularia  elegans  Clark.  San  Diego,  Cal.  (Dr.  15.  Palmer). 

Thamnocnidia  tubiilaroides  A.  Ag.  Bay  of  San  Francisco,  Cal.  (A.  Agassiz). 


*  Tlie  Annals  and  Magazine  of  Natural  History,  Series  3,  No.  XXVIII,  April,  1860. 
Descriptions  of  new  species  of  Hydroids  from  the  Californian  Coast.  By  Andrew 
Murray. 

\  Illustrated  Catalogue  of  the  Museum  of  Comparative  Zoology.  No.  II.  North 
American  Acalephre.     By  Alexander  Agassiz.     1805.^ 


^S".  F.  Clark — Ilydroids  of  the  Pacific  Coast. 


251 


Par3'plia  microcephala  A.  Ag. 
Bimeria  gracilis  Clark. 
Bougainvillia  Mertensii  Agassiz. 
Eudendrium,  sp. 
Campauularia  everta  Clark. 

Campanularia  fusiformis  Clark. 
Campanularia  cyliudrica  Clark. 
Laomedea  rigida  A.  Ag. 
Laomedea  Pacifica  A.  Ag. 

Lafoea  dumosa  Sars. 
Halecium  tenellum  Hincks. 
Sertularia  angiiina  Trask. 

Sertularia  anguina,  var  robusta  Clark. 

Sertularia  argeutea  E.  and  S. 
Sertularia  pumila  Linn. 
Sertularia  Greenei  Murray. 


Bay  of  Sau  Francisco,  Cal.  (A.  Agassiz). 

Sau  Diego,  Cal.  (E.  Palmer). 

Bay  of  San  Francisco,  Cal.  (A.  Agassiz). 

Santa  Cruz,  Cal.  (C.  W.  Anderson). 

San  Diego,  Cal.  (H.  Hemphill),  to  Vancouver 

Island  (J.  M.  Dawson). 
Vancouver  Island  (J.  M.  Dawson). 
Santa  Cruz,  Cal.  (C.  W.  Anderson). 
Bay  of  San  Francisco,  Cal.  (A.  Agassiz). 
Gulf  of  Georgia  (A.  Ag.)  to  Bay  of  San 

Francisco  (A.  Agassiz). 

San  Diego,  Cal.  (Dr.  E.  Palmer). 

Santa  Cruz,  Cal.  (C.  "W.  Anderson),  to  Van- 
couver Island  (J.  M.  Dawson). 

San  Diego,  Cal.  (H.  Hemphill),  to  Vancouver 
Island  (J.  M.  Dawson). 

Santa  Barbara,  Cal.  (Mrs.  EUwood  Cooper). 


Sertularia  furcata  Trask. 

Sertularia  corniculaia  Murray. 
Sertularella  turgida  Clark  (Trask). 

Plumularia  setacea  Lamarck. 


Santa  Barbara,  Cal.  (Mrs.  P]llwood  Cooper), 
to  Vancouver  Island  (J.  M.  Dawson). 

San  Diego  (Dr.  E.  Palmer),  to  Bay  of  San 
Francisco  (J.  B.  Trask). 

Bay  of  San  Francisco  (A.  Murray). 

San  Diego,  Cal.,  to  Vancouver  Island  (J.  M. 
Dawson). 

San  Diego,  Cal.  (Dr.  E.  Palmer),  to  Van- 
couver Island  (J.  M.  Dawson). 
Aglaophenia  struthionides  Clark  (Murray).  San  Diego,  Cal.  (D.  C.  Cleveland),  to  Van- 
couver Island  (Miss  Mitchell). 

This  list  of  twenty-four  species  is  very  small  compared  with  that  of  the 
eastern  coast,  from  Maine  to  New  York,  the  fauna  of  the  latter  region 
containing  five  times  as  many  species  as  that  of  the  former,  notwith- 
standing that  the  i-egion  included  on  the  western  coast  is  over  thirteen 
hundred  miles  in  length,  while  that  of  the  New  England  coast  is  only 
about  eight  hundred.  It  should  be  borne  in  mind  however  that 
most  of  the  collecting  on  the  Pacific  coast  has  been  done  along  the 
shore,  the  dredge  having  been  little  used,  and  there  is  little  doubt  that 
when  the  fauna  has  been  more  thoroughly  investigated  the  number 
of  Hydroids  may  be  at  least  doubled.  Such  a  variety  as  exists  on 
the  New  England  coast  can  hardly  be  expected  from  our  Pacific 
shores  south  of  Vancouver  Island,  for  the  waters  there  do  not  afford 
the  same  diversity  in  temperature. 


252  S.  F.  Clark — Ilydroids  of  the  Pacific  Coast. 

Bimeria  (?)  gracilis,  sp.  nov. 
riate  XXXVIII,  figure  3. 

Stems  clustered,  rooted  by  a  creeping  stolon,  erect,  simple,  delicate, 
not  divided  by  distinct  joints,  thickly  branched ;  branches  suberect, 
the  larger  ones  reaching  to  the  end  of  the  stem  and  resembling  the 
main  stalk,  the  smaller  ones  bear  but  one  or  two  hydranths  and  are 
also  unjointed;  perisarc  extending  over  the  hydranths  and  partially 
covering  the  tentacles,  annulated  at  the  base  of  each  branch  and 
branchlet.  Sporosacs  developed  from  the  hydrophyton,  a  single  one 
at  the  base  of  each  hydranth-bearing  branchlet,  oval  or  ovate,  sup- 
ported by  a  short  peduncle  consisting  of  one  or  two  annulations. 
Hydranths  large,  tapering  uniformly  from  the  distal  end  to  the  base, 
provided  with  about  ten  or  twelve  tentacles  and  with  a  large, 
rounded  or  slightly  conical  proboscis.  Height  of  best  specimen, 
55"'"'. 

Collected  on  the  jtiles  of  wharves  at  San  Diego,  Cal.,  by  Dr.  E. 
Palmer,  18'75. 

Our  specimens  were  not  in  a  good  condition  when  they  arrived, 
having  been  crowded  in  a  tin  can  with  many  other  things,  which 
pressed  them  all  out  of  shape,  and  the  quantity  of  alcohol  not  being 
sufficient  to  preserve  so  much  animal  matter,  the  hydi-oids  suffered 
considerably;  the  hydranths  and  sporosacs  especially  were  in  a  very 
worn  and  mutilated  state.  It  is  not  easy  to  determine  just  how  far 
the  perisarc  extends  upon  the  hydranth,  but  it  certainly  covers  tlie 
body  of  the  latter,  and  it  must,  I  think,  be  developed  over  a  portion 
of  the  tentacles,  for  after  soaking  them  in  a  dilute  solution  of  caustic 
potash  for  forty-eight  hours  the  tentacles  still  retained  their  normal 
position,  nor  did  they  show  any  decrease  in  size.  The  potash  seemed 
to  act  very  slowly,  for  after  being  in  the  warm  solution  forty-eight 
hours  the  hydranths  were  not  entirely  dissolved  out.  The  fact  of 
the  tentacles  being  unaftected  would  seem  to  indicate  that  they  are 
entirelv  protected  by  chitin,  but  tentacles  so  protected  would  be  of 
little  or  no  use  to  the  animal,  and  I  think  it  more  j)rol)able  that  the 
distal  portions  are  free  and  may  be  contracted  into  the  basal  covering. 
It  is  impossible  to  determine  from  our  specimens  how  the  tentacles 
are  held,  whethei-  in  a  single  erect  verticil  as  in  Garveia  or  with 
each  alternate  tentacle  depressed,  as  in  Bimeria  vestita  of  Wright. 
With  such  imi)erfect  data  I  feel  some  doubt  about  placing  this  species 
in  the  genus  Bimeria,  and  only  do  so  provisionally. 


>S'.  F.  Clark — Ilydroids  of  the  Pacific  Coast.  253 

Tubularia  elegans,  sp.  nov. 
Plate  XXXVIII,  figure  2. 

Stems  clustered,  rooted  by  a  creeping  stolon,  erect,  unbranched, 
more  or  less  annulated  at  intervals  toward  the  base.  Hydranths 
large,  with  about  thirty  tentacles  in  the  proximal  set  and  twenty  to 
twenty-four  in  the  distal.  Gonophores  borne  in  clusters  just  inside 
the  proximal  tentacles,  twelve  to  twenty  in  a  cluster,  each  of  the 
larger  ones  crowned  with  four  conical  tubercles.  Height  of  tine.st 
specimen,  75""". 

Collected  on  the  piles  of  the  wharf  at  San  Diego,  by  Dr.  E.  Palmer 
1875.  Intermingled  with  it  and  often  attached  to  it  were  numerous 
shoots  of  Blmeria.  Many  of  the  young  had  attached  themselves  to 
the  parent  stalk,  giving  at  first  sight  the  appearance  of  branching 
stems.  , 

The  specimens  from  which  this  species  is  described  were  crowded  in 
the  same  can  with  the  Bimeria  described  above,  and  are  in  the  same 
dilapidated  condition.  There  is  a  Tubularian,  Tha/mnocnidla  tuhular- 
oides,  from  the  Bay  of  San  Francisco,  described  by  A.  Agassiz  (Cat. 
of  N.  A.  Acalephje,  p.  196),  which  he  says  "is  readily  distinguished 
from  its  eastern  congeners  by  the  stoutness  of  the  stem  and  large  size  of 
the  head."  The  description  is  a  very  meagi-e  one,  but  from  these  two 
characters  I  conclude  that  it  must  be  distinct  from  T.  elegans,  for  the 
latter  spetaes  has  neither  a  stouter  stem  nor  larger  head  than  Tham- 
nocnidia  spectahilis  of  the  New  England  coast. 

Eudendrium,  sp. 
Plate  XXXVIII,  figure  1. 

We  have  also  received  from  the  California  coast  the  perisarc  or 
chitinous  portion  of  what  I  take  to  be  a  species  of  Eudendrium. 

Stems  stout,  erect,  dark  horn  color,  strongly  annulated  throughout, 
rather  sparingly  branched  ;  branches  sub-erect,  springing  from  all 
sides  of  the  stem  and  much  divided.  Hydranths  borne  at  the  ex- 
tremity of  the  short  ramuli.  The  entire  perisarc  is  strongly  ringed, 
giving  it  a  close  resemblance  to  the  trachete  of  an  insect.  Height  of 
largest  specimen,  80"'"'" 

Santa  Cruz,  Bay  of  Monterey,  Cal., — Dr.  C.  W.  Anderson. 

Campanularia  everta,  sp.  nov. 
Plate  XXXIX,  figure  4. 
Stems  rather  stout,  arising  at   intervals  from   the   creeping  stolon, 
with  two  annulations  at  the  base  of  the  hydrothecte,  the  lower  one 


254  S.  F.  Clark— Hydr Olds  of  the  Pacific   Coast. 

smaller  than  the  upper;  the  remainder  of  the  stem  has  a  wavy  outline 
or  is  slightly  annulated,  Hydrothec^  broadly  campanulate,  not 
deep,  tapering  more  or  less  gradually  from  the  distal  end  to  the  base, 
the  rim  strongly  everted  and  bearing  about  fifteen  rather  shallow 
teeth.  Gonothecje,  large,  turgid,  nearly  cylindrical,  tapering  a  little 
at  the  base,  borne  on  short,  stout  peduncles  and  with  the  aperture 
terminal,  small  and  cylindrical. 

Found  creeping  on  an  Alga  from  San  Diego,  Cab, — H.  Hemphill. 

This  is  a  very  pretty  form  and  may  readily  be  distinguished  by  the 
broad  hydrothecae  with  their  strongly  everted,  toothed  rims.  The 
peculiar  shape  of  the  gonothecte  is  also  very  characteristic. 

Campanularia  cylindrica,  sp.  nov. 
Plate  XXXIX,  figures  1-r'. 
Stems  are  simple,  unbranched  pedicels,  of  very  variable  length, 
more  or  less  annulated  over  the  entire  length  and  with  a  single  well- 
marked  ring  at  the  base  of  the  hydrothecje,  rooted  by  a  creeping, 
twisted  stolon.  Hydrothecte  campanulate,  nearly  cylindrical,  taper- 
ing but  very  slightly  toward  the  base,  varying  greatly  in  depth,  rim 
armed  with  about  fifteen  very  shallow,  sharply  pointed  teeth.  The 
gonothecse  also  show  considerable  variation  in  size,  there  being  occa- 
sionally one  or  two  which  are  at  least  twice  the  size  of  the  ordinary 
form;  they  are  subfusiform,  tapeiing  sliglitly  more  toward  the  proxi- 
mal than  the  distal  end,  supported  on  short  pedicels  with  one  or  two 
annulations. 

Campanularia  fusiformis,  sp.  nov. 
Plate  XXXIX,  figures  2-2-. 

Hydrocaulus  simple,  creeping,  bearing  the  pedicels  at  irregular 
intervals;  ])edicels  of  variable  length,  usually  two  or  three  times 
the  length  of  the  hydrothec;^,  never  more  than  six  times  their 
length,  with  a  more  or  less  w^avy  outline.  Hydrotheca?  small,  deeply 
campanulate,  tapering  at  the  base,  rim  ornamented  witli  about  twelve 
stout,  shallow,  acute  teeth,  a  single  distinct  annulation  at  the  base. 
GonotheciB  small,  fusiform,  constricted  at  both  ends,  sessile,  aperture 
small,  terminal. 

Vancouver  Island, — J,  M.  Daw^son.  Found  growing  on  Sertularia 
angidna  var.  rohusta. 

This  species  is  closely  allied  to  C.  cylindrica  of  the  Californian 
coast  from   which  it  may  be  distinguished  by  the  size  of  the  hydro- 


S.  F.  Clark — Sydroids  of  the  Pacific  Coast.  255 

thecffi  and  by  their  shajjc,  not  being  rounded  at  the  base ;  by  the  form 
of  tlie  gonotliectp,  wliicli  are  sessile  and  liave  a  circular  terminal 
aperture. 

Found  creeping  on  the  old  stems  of  a  MtdendriuniWke  form, 
taken  at  Santa  Cruz,  Cal.,  Bay  of  Monterey,  by  Dr.  C.  W.  Anderson. 

The  variation  in  the  lengtli  of  the  stems  is  very  great ;  sometimes 
they  are  aboiit  equal  to  the  length  of  the  hydrothecjje,  and  again 
they  will  be  five  or  six  times  that  length.  The  stolon  is  quite 
uniformly  twisted  and  is  at  least  twice  the  diameter  of  the  stems. 

Halecium  tenellum.  Hincks. 

Halecium  tenellum  Hincks,  Annuls  and  Map;,  of  Nat.  Hist.,  3,  VIII.  252,  pi.  VI. 

Plate  XXXIX,  figure  5. 
Some  very  good  specimens  of  this  delicate  species  have  been 
received  from  San  Diego.  There  were  no  gonothecfe  but  the  hydro- 
some  is  so  exactly  similar  to  our  New  England  specimens  and  to  the 
figure  and  description  of  Hincks  that  I  do  not  hesitate  to  call  it  the 
same.  A  glance  at  our  figure  will  show  how  exactly  it  corresponds. 
Found  parasitic  on  a  species  of  Bimeria,  collected  on  the  piles  of 
wharves,  San  Diego,  Cal., — Dr.  E.  Palmer,  18Y5. 

Sertularia  anguina  Trask. 

Sertularia  anguina  Trask,  Proc.  Cal.  Acad.  Nat.  Sci.,  112,   Plate  V,  fig.  1.     March 

30,  1857. 
Sertularia  Inhrata  Murray,  Ann.  and  Mag.  for  April,  1860,  250,  Plate  XI,  fig.  2. 

Plate  XL,  figures  1,  P,  2. 
Stems  clustered,  simple,  erect,  straight  from  the  proximal  end  to 
the  first  branch,  above  the  first  branch  flexuous,  becoming  more  and 
more  so  toward  the  distal  end,  sparingly  branched,  divided  by  trans- 
verse joints  into  short  internodes,  those  below  the  first  branch  bearing 
a  single  pair  of  nearly  opposite  hydrothecre,  while  those  above  the 
first  branch  have  three  hydrotheese  and  give  origin  to  a  single  branch  ; 
branches  regularly  alternate,  ascending,  slightly  curved,  mostly  short, 
a  few  have  a  much  larger  growth  and  exactly  imitate  the  main  stems 
in  every  particular;  color  corneous.  Hydrotheca3  nearly  opposite, 
somewhat  flask-shaped  or  tapering  evenly  to  the  distal  end  with- 
out any  constriction  or  flask-shaped  neck ;  aperture  usually  entire, 
slightly  oblique,  facing  toward  the  stem,  or  with  the  outer  margin 
much  more  produced  than  the  inner  and  in  some  cases  showing  a  dis- 


256  S.  P.  Clark — Itydroids  of  the  Pacific  Coast 

tinctly  sinuous  outline.  Gonothecse  unknown.  Height  of  largest 
specimen,  75"'"'.  Plentiful  on  a  large  species  of  Mytilus  from  Mon- 
terey, Tomales  Pt.,  Punta  Reyes,  and  on  old  shells,  Bay  of  San  Fran- 
cisco (Dr.  Trask)  ;  Santa  Cruz, — Dr.  Anderson;  Vancouver  Island, 
— J.  M,  Dawson. 

Our  specimens  of  S.  anguina  agree  so  closely  with  Hinck's  descrip- 
tion and  figures  of  S.  filicula  that  I  cannot  separate  the  trophosomes, 
but  the  gonosomes  being  unknown,  I  prefer  to  let  the  species  remain 
distinct  rather  than  to  unite  them  on  such  incomplete  data.  Murray 
also  noticed  the  similarity  to  *S'.  filicula  although  he  only  possessed 
"  a  minute  portion  without  vesicles." 

Dr.  Trask  says  of  his  specimens,  "  Their  affinity  is  witli  that  of  8. 
fallax  of  Johnston  more  nearly  than  with  any  other  species  with 
which  I  am  acquainted."  He  could  not  have  known  (^f  ^i.  filicula  at 
that  time  or  he  would  at  once  have  noticed  the  much  closer  resem- 
blance to  that  form.  Pie  also  says  that  his  specimens  have  four 
hydrothecie  between  each  pair  of  branchlets,  while  ours  have  but 
three:  one  pair  opposite  each  othei-  and  one  odd  cell  in  the  axil  of  the 
branch.  His  description  and  figure  agree  so  well,  however,  in  evei'y 
other  respect  that  I  am  inclined  to  regard  this  as  an  error  of  observa- 
tion. 

This  description  has  been  made  from  specimens  which  were  dried 
before  they  were  sent  to  iis  and  have  since  been  soaked  out  in  warm 
water.  The  perisarc  being  very  stout  and  durable  I  do  not  think 
that  it  can  have  changed  to  any  great  extent. 

Sertularia  anguina,  variety  robusta  Clark. 
Plate  XL,  figures  3,  4,  5. 

The  variety  robusta  differs  from  the  ordinary  form  in  having  a  stouter 
stem,  larger  hydrotheca%  longer  pinnjie,  and  in  being  in  every  way  a 
much  larger  and  stouter  form.  The  mode  of  growth,  the  branching, 
the  shape  and  arrangement  of  the  hydrothecae  are  the  same  as  in  the 
normal  form.  Gonothecae  borne  on  the  pinnae,  more  or  less  fusiform, 
arising  from  just  below  the  hydrotheca^,  distal  extremity  slightly 
curved  to  one  side,  the  terminal  aperture,  large,  circulai'.  Length  of 
largest  specimens,  100""". 

San  Diego,  Cal., — Henry  Hemphill ;  taken  from  kelp  roots  washed 
ashore  during  a  storm. 

San  Diego,  Cal.,— D.  C.  Cleveland,  1875;  Santa  Cruz,  Cal.,  Bay  of 
Monterey, — Dr.  C.  W.  Anderson  ;  Vancouver  Island, — J.  M.  Dawson. 

This  variety  is  very  similar  to  S.  abietina  of  Linmeus  in   many 


*S'.  F.  Clafh — Ilydrokh  of  the  Pacific  CoaM.  '251 

respects.  It  lias  the  same  mode  of  growth,  the  same  robust  habit, 
tlie  same  style  and  airangement  of  hydrothecse.  There  is  quite  a  dif- 
erence  in  the  natural  size  figures  of  .S.  ahietlna  given  by  Uincks  and 
by  Johnston.  Our  specimens  from  the  New  England  coast  agree  very 
well  with  Johnston's  figure,  which  is  just  about  twi(!e  the  size  of 
Hincks'  H""ure. 


Sertularia   argentea  Ellis  and  Solander  (Linn.) 

Three  fine  specimens  of  this  widely  distributed  species  have  been 
found  at  Santa  Barbara,  California ;  they  are  in  good  condition  and 
loaded  wdth  gonothectB.  The  only  characteristic  which  shows  any 
variation  is  the  gonotheca?,  which  are  proportionally  a  trifle  longer 
and  also  have  the  orifice  a  little  larger  than  in  our  east  coast  speci- 
mens. This  slight  difference  being  the  only  one  and  this  character 
varying  considerably  in  the  same  specimen,  I  should  not  think  of  sep- 
arating them. 

Santa  Barbara,  Cal., — INtrs.  Ellwood  Cooper.  Height  of  largest 
specimen,  160""". 

Sertularia  Greenei  Murray. 

Sertularia  tricuspidata  Murray,  Ann.  and  Mag.  for  April,  I860,  p.  250,  PI.  XI,  lig.  1. 

Sertularia  Greenei  Murray,  Ann.  and  Mag.,  v,  p.  504,  1860. 

Cotulina  Greenei  A.  Aga.ssiz,  Cat.  of  N.  Amer.  Acalepha?,  1865,  p.  147. 

Plate  XXXVIII,  figure  6. 

Stems  erect,  slender,  densely  clustered,  simple,  thickly  branched, 
basal  portion  straight,  above  the  first  branch  becoming  slightly  flex- 
uous,  forming  a  graceful  arc  between  each  two  branches,  color  cor- 
neous, usually  darkest  at  the  base  ;  joints  placed  at  right  angles  to 
the  stem  and  very  irregularly  distributed,  forming  iuternodes  which 
bear  from  one  to  eight  pairs  of  hydrothecEe  ;  branches  alternate,  erect, 
many  of  them  short;  some  of  the  lower  ones  equal  in  length  to  the 
main  stem  and  closely  resembling  it  in  every  respect;  others  from 
the  middle  portion  of  the  stem  are  of  a  medium  length  aiul,  like  the 
longest  branches  from  the  lower  part  of  the  stem,  reach  to  the  extrem- 
ity of  the  main  stem  forming  a  corymb-like  structure,  Tlie  branch- 
lets,  like  the  branches,  are  mostly  short,  but  a  few  are  of  considerable 
length,  extending  to  the  ends  of  the  branches.  Ilydrothecse  sub-alter- 
nate, tapering  uniformly  to  the  distal  end,  Avith  oblique,  toothed 
apertures,  which  face  toward  the  stem  ;  on  the  outer  edge  of  the 
aperture  are  two  large,  prominent  teeth  separated  by  a  deep  notch. 

Trans.  Conn.  Acad.,  Vol.  III.  33  June,  187G. 


258  ;S'.  F.  Clark — Hydroicts  of  the  Pacific  Coast. 

Gonotheciu  borne  in  rows  on  the  upper  sides  of  the  branclilets  ;  the 
upper  j>ortion  cylindrical,  the  proximal  half  tapering  toward  the  base, 
aperture  terminal,  in  a  small  cylindrical  process  elevated  from  the 
center  of  the  distal  end.     Height  of  largest  specimens,  90""". 

Bay  of  San  Francisco,  Cal., — Murray  ;  Santa  Cruz,  Cal., — Dr.  C.  W. 
Anderson;  Santa  Barbara,  Cal., — Mrs.  EUwood  Cooper;  Vancouver 
Island, — J.  M.  Dawson. 

This  is  an  interesting  form  as  it  is  the  only  member  of  the  Sertu- 
laridm  on  the  American  coast  having  the  peculiar  aperture  to  the 
goriothecae,  by  Agassiz  called  bottle-shaped,  though  it  is  by  no  means 
an  uncommon  form  among  our  CainjKinidar'uloe, —  Obelia  yelatlnosa, 
0.  genicnlata  and  0.  dichotoma  having  the  same  general  form  of 
gonotliecae. 

A  peculiar  discrepancy  occurs  in  the  descriptions  of  Murray  and 
A.  Agassiz  in  regard  to  the  number  of  teeth  on  the  rims  of  the 
hydrothecae  ;  the  former  describes  them  with  three  teeth,  the  centi'al 
one  being  larger  than  the  two  lateral,  while  Agassiz  describes  them 
with  four,  two  prominent  exterior  points  and  two  smaller  ones  near 
the  stem.  We  have  quite  a  large  supply  of  specimens  in  a  good  state 
of  preservation  and  after  having  carefully  examined  them  all,  I  cannot 
find  a  single  hydrotheca  that  would  afford  any  reason  for  changing 
the  above  description  of  tvio  teeth  upon  the  rim  of  each  cell. 

I  should  judge  from  Murray's  figure  that  his  specimens  were  not 
well  preserved  and  by  contracting  had  thrown  out  the  inner  margin 
of  the  rim,  giving  it,  in  some  views,  the  appearance  of  a  tooth.  But 
how  he  made  out  one  tooth  to  be  much  larger  than  the  other  two,  I 
am  at  a  loss  to  understand.  And  the  fact  of  Agassiz  having  seen 
four  teeth  I  am  at  present  unable  to  account  for. 

Sertularia  furcata  Trask. 

Sertularia  furcata  Trask,  Proc.   Cal.   Acad.   Nat.  Sci.,  Mar.  30,  1857,  112,  Plate  V, 
figs.  2,  a,  b,  0,  d,  e. 

Plate  XXXIX,  figure  3. 

Stems  short,  unbranched,  rooted  by  a  creeping  stolon,  simple,  spread- 
ing in  every  direction  forming  dense  verticillated  clusters  around  the 
pieces  of  fucus  on  which  it  is  usually  found,  attached  to  the  stolon 
by  a  short,  slender,  twisted  process  about  the  length  of  an  internode, 
divided  by  transverse  joints  into  short  regular  internodes  each  bearing 
a  single  pair  of  hydrothecte,  color  corneous.  Hydrothecije  oppo- 
site, deeply  immersed  in  the  stem,  with  two  large,  sharp  teeth  on 


iS.  F.  Clark — Hydro  ids  of  the  Pacific  Coast.  259 

the  outer  margin  and  a  large  aperture  generally  reaching  to  the 
stem.  Gonotlieca3  large,  sessile,  generally  borne  near  the  base  of  the 
steins  though  occasionally  found  scattered  over  the  entire  length,  of 
an  elongated  oval  form,  sometimes  slightly  compressed,  with  a  large 
circular,  terminal  aperture.     Height  of  largest  s|)ecimen,  45""". 

Bay  of  San  Francisco  and  Farallone  Islands, — Trask ;  Santa  Cruz, 
Cal.,  Bay  of  ^lonterey, — C.  W.  Anderson  ;  San  Diego,  Cal., — Dr.  E. 
Palmer  ;  Santa  Barbara,  Cal., — Mrs.  Ellwood  Cooper  ;  Santa  Barbara, 
Cal.,— Dr.  L.  X.  Dimmick. 

S.  furcata  seems  to  be  more  nearly  allied  to  aS',  Greenei  than  to 
any  other  Sertularian  of  the  west  coast  known  to  us,  both  having 
the  same  style  of  hydrothecte,  arranged  in  about  the  same  manner 
and  with  similarly  toothed  apertures.  It  is  the  same  style  seen  in  S. 
operculata  of  Linnteus. 

-iS'.  furcata  may  be  readily  <listinguished  from  S.  (xreenei  by  its 
entirely  different  gonothecfe,  by  the  different  size  of  the  aperture  in 
the  hydrothccae,  by  the  extent  to  which  the  hitler  are  immei-sed  in 
the  stem  and  by  the  habit  or  mode  of  growth.  In  general  appearance 
it  strongly  reminds  one  of  the  Sertalaria  puudla  of  the  New  England 
coast. 

Sertularella  turgida  <'iaiis  (Trask). 

Sarlularia  turgida  Trask,  Proc.  Cal.  Acad.  Nat.  Sei..  Mar.  30,  1857,  11.".,  Plate  IV, 
fig.  1. 

Sertularia  turgida  A.  Agassiz,  Cat.  N.  Am.  Acalepha3,  p.  145,  1865. 
Plate  XXXVIII,  figures  4,  5. 

Stems  attached  by  a  creeping  stolon,  sparingly  branched,  attached 
to  the  stolon  by  a  pedicel  consisting  of  three  or  four  rings,  short, 
stout,  simple,  spreading  in  every  direction  from  the  branches  of  fucus 
and  pieces  of  laminaria  which  seem  to  be  the  favorite  stations  of  this 
species,  divided  by  oblique  joints  into  shori,  stout  internodes  each 
bearing  a  single  hydrotheca,  color  light  corneous  ;  branches  stout, 
erect,  usually  about  half  the  length  of  the  main  stem  and  very  irregu- 
larlv  arranged,  in  some  cases  alternately,  in  others  all  the  branches 
spring  from  one  side  of  the  stem  and  sometimes  there  seems  to  be 
no  regular  arrangement.  Hydrotheca?  large,  full,  alternate,  deeply 
immersed  in  the  stem,  the  inner  angle  of  the  proximal  end  extending 
more  deeply  into  the  stem  than  the  outer,  aperture  large,  armed  with 
three  stout  teeth,  two  of  which  are  larger  than  the  other  and  are 
situated  on  the  outer  side  of  the  rim,  facing  the  stem,  the  third  tooth 


260  iS'.  F.  Clark — Hydroids  of  the  Pacific  Coast. 

is  on  the  inner  margin  of  the  rim  midway  between  the  other  two. 
Gonothecae,  arising  in  the  axils  of  the  hydrotheca?,  are  large  and  of 
two  forms ;  the  larger  form,  similar  to  the  gonotheea  of  Sertu- 
larella  polyzonias  Gray  (Linn.),  is  obovate,  sessile,  armed  with  a 
few  stout,  blunt  spines  around  the  distal  end,  aperture,  terminal 
and  at  the  outer  end  of  a  small  cylindrical  process  formed  by  a 
constriction  or  a  very  sudden  tapering  near  the  extremity  and 
surrounded  by  a  number  of  the  largest  spines  ;  the  smallei'  form  is 
supplied  Avith  about  twice  as  many  spines  as  the  larger  foi'm  and  is 
shorter  and  proportionally  broader,  the  broadest  portion  being  nearer 
to  the  distal  end  ;  this  variation  in  form  undoubtedly  indicates  a  sexual 
difference,  the  smaller  form  proba1>ly  being  the  male  find  the  larger 
the  female  gonothecje ;  both  forms  have  the  surface  more  or  less 
roughened  by  transverse  Avrinkles.  Length  of  largest  specimen, 
38""". 

Bay  of  San  Francisco,  Monterey,  Tomales  Point,  Cal„  on  mollusca 
and  alga^, — Trask  ;  Santa  Ci-uz,  Bay  of  Monterey,  Cal.,— Dr.  C.  W. 
Anderson ;  San  Diego,  Cal., — D.  C.  Cleveland  ;  Vancouver  Island, 
— J.  M.  Dawson. 

The  nearest  ally  of  S.  turglda  is  the  ^S.  polyzonias  of  Gray,  to 
which  in  many  respects  it  bears  a  striking  resemblance. 

Hydrallmania  Franciscana  Clark  (Trask). 

Plumularia  Franciscana  Trask,  Proc.  Cal.  Acad,  of  Nat,  Sci.,  vol.  i,  p.  113,   PI.   IV, 

fig.  3. 
Plumularia  gracilis  Murray,  Ann.   and  Mag.  of  Nat.  Hist,  for  April,  1800,  p.  251, 

PI.  XII,  fig.  1. 

Trask  and  Murray  both  had  representatives  of  a  species  which  they 
referred  to  the  genus  Plwnularia  and  whicli,  from  their  descriptions 
and  figures,  undoul)tedly  belongs  to  Hinck's  genus  Ilydmllmania, 
though  at  the  time  their  descriptions  were  published,  this  genus  had 
not  been  recognized.  This  sjiecies  is  certainly  very  close  to  II. 
falcata  of  Hincks,  but  Murray,  who  had  an  opportunity  of  comparing 
the  two,  says  they  are  distinct. 

Unfortunately  we  have  had  no  specimens. 

Bay  of  San  Francisco,  Cal.,  among  rejectamenta  on  the  beach, 
—Trask. 


>S.  F.  Clark — Hj/droids  of  the  Pacific  Coast,  261 

Plumularia  setacea  Lamarck. 

Sertularia  piiinata,  [3,  Linn.,  Syst.  Nat.,  11!  12. 

Sertularia  setacea  Pallas,  Elench.,  p.  148. 

Plumularia  setacea  Lamk..  An.  s.  Vert.  (2d  ed.),  ii,  165. 

Plate  XLI,  figures  1,  2. 

Stems  simple,  slender,  erect,  rooted  by  a  creeping  stolon  and 
divided  by  transverse  joints  into  short  internodes  of  uniform  size, 
regularly  branched  ;  pinn.e  alternate,  regulai-ly  arranged,  one  from 
each  internode,  arising  from  the  stem  by  a  pi-ominent  process  pro- 
duced from  the  outer  and  upper  side  of  each  internode,  divided  by  trans- 
verse or  slightly  oblique  joints  into  internodes  of  two  sizes  arranged 
alternately.  In  large  specimens  150"'"'.  to  800'""'.  long,  the  main  stems 
are  considerably  branched,  the  branches  alternately  arranged  and 
clustered,  extending  quite  or  nearly  to  the  distal  end  of  the  stem; 
the  branches  give  off"  l)ranchlets,  which  like  themselves  resemble  the 
main  stems  in  every  particular.  Hydrotheca?  with  an  even  rim,  small, 
borne  on  the  larger  sized  internodes  of  the  pinna>.  Nematophores 
compound,  those  on  the  pinn;v  not  quite  equal  in  length  to  the  hydro- 
thecfe,  those  on  the  main  stems  a  little  longer  than  the  hydrothecae; 
three  on  each  internode  of  the  stem,  two  in  the  axil  of  each  pinna, 
one  on  the  opposite  side  of  the  internode  near  the  bnse,  one  only  on 
the  upper  side  of  the  smaller  joints  of  the  pinn{\3  and  three  on  the- 
larger  joints,  one  just  below  the  hydrotheca,  and  one  on  each  side  of 
the  apertui-e  Gonotheca^  sessile,  l)orne  in  the  axils  of  the  pinna* ; 
female  elongate  oval,  produced  at  the  distal  end  into  a  tubular  neck 
with  a  discoidal,  terminal  orifice ;  male,  smaller  than  the  female, 
fusiform,  and  with  a  much  smaller  aperture. 

Santa  Cruz,  Cal.,  — C.  W.  Anderson;  San  Diego,  Cal, — Dr.  H  Pal- 
mer; San  Diego,  Cal., — H.  Hemphill;  Vancouver  Island, — Dawson. 

Most  of  our  specimens  consist  of  dense  clusters  of  the  delicate 
shoots,  about  50'""''  to  80"""*  long,  and  usually  attached  to  some  large, 
coarse  alga.  Ellis'  old  name  of  "  iSea  Bristle.^''''  was  well  chosen,  for 
it  conveys  quite  an  accurate  idea  of  the  appearance  of  these  smaller 
forms.  The  larger  forms  are  more  branched,  usually  of  a  darker 
color  and  have  a  closer  resemblance  to  hair  than  to  bristles;  one  of 
our  largest  specimens  from  San  Diego  consists  of  a  tuft  200"""-  in 
length  composed  of  about  three  hundred  branched  shoots  ;  this  liad 
been  washed  ashore  and  was  found  by  Dr.  Palmer;  a  still  larger 
specimen  was  dredged  off  San  Diego  in  six  to  ten  fathoms  by  IVIr. 
Hemphill,  which  measures  .300"""-  in  length  and  forms  a  thick  cluster 
of  about  a  thousand  shoots. 


262  *S'.  F.  Clark — Uydrolds  of  the  Pacific  Coast. 

Aglaophenia  struthionides  Clark  (Murray). 

Flumulari'i  stridhmmles  Murray.  Ann.  and  Mag.  of  Nat.  Hist,  for  April,  1870,  251, 

Plate  XII,  fig.  2. 
Arjlanphenia  franciscana  A.  Agassiz,  Cat.  N.  A.  Acalephai,  p.  140,  1865. 

Plate  XLI,  figures  3-3''. 

Stems  rooted  by  a  creeping  stolon,  simple,  erect  or  spreading  in 
every  direction,  divided  by  slightly  oblique  joints  into  very  short 
internodes  of  equal  length,  each  bearing  a  single  pinna,  varying 
from  the  lightest  to  the  darkest  horn-color;  shoots  tall,  stout,  plumose, 
tapering  slightly  toward  the  base,  the  distal  end  abruptly  pointed  ; 
pinna'  slightly  curved,  sub-erect,  unbranched,  not  in  the  same  plane, 
the  sides  bearing  the  hydrothecie  curving  toward  each  other,  divided 
into  short  internodes  by  slightly  oblique  joints,  each  internode  bear- 
ing a  single  hydrotheca.  Hydrotheca^  large,  cu}>shaped,  expanding 
toward  the  distal  end,  aperture  large,  patulous,  rim  denticulated, 
armed  usually  with  eleven,  sometimes  nine,  sharp,  uneven  teeth. 
Nematophores  tubular,  the  lateral  ones  of  medium  size,  projecting 
ear-like  from  the  sides  of  the  hydrothecae,  the  anterior  one  long, 
adnate  for  the  greater  part  of  its  length,  free  near  the  distal  end, 
extending  nearly  or  quite  to  the  edge  of  the  toothed  rim,  aperture 
small,  discoidal,  terminal ;  those  upon  the  corbula3  are  a  trifle  larger 
than  the  lateral  ones  and  are  arranged  in  transverse  rows,  the  ends 
of  which  do  not  meet.  Corbuhe  large,  cylindrical,  with  numerous 
rido-es  (ten  to  sixteen)  composed  of  oblique  rows  of  nematophores ; 
usually  from  two  to  six  hydrotheca?  at  the  base  of  the  corbula.  In 
luxurious  specimens  the  corbula-  are  very  abundant,  there  being 
between  seventy  and  eighty  t)n  a  single  shoot.  Length  of  largest 
specimen,  150"""" 

Bay  of  San  Francisco,- -Trask ;  San  Francisco,  Cal.,— A.  Agassiz; 
Santa  Barbara,  Cal.,— L.  F.  Dimmick  ;  Santa  Barbara,  Cal.,— Mrs. 
EUwood  Cooper ;  Santa  Cruz,  Cal.,  Bay  of  Monterey, — C.  W.  Ander- 
son* San  Diego,  Cal.,— D.  C.  Cleveland;  Vancouver  Ishmd, — Miss 
Mitchell ;  Vancouver  Island, — J.  M.  Dawson. 

In  the  various  lots  of  Hydroids  which  we  have  received  from  the 
western  coast,  this  species  has  always  been  the  most  abundant.  It 
seems  to  be  as  common  and  as  widely  disti'ibuted  on  the  western 
coast  of  the  United  States  as  tSertularia  puniila  is  upon  the  eastern 
coast.  Both  are  also  very  often  found  parasitic  on  algiie,  but  A.  stru- 
thionide-s  is  often  found  in  deeper  water  than  N.  pui/td-a. 


S.  F.  Clark— iTydroich  of  flic  Pacific  Coast.  263 

As  ^Murray  r(>inarl<s,  tliis  species  is  nearly  allied  to  Phinmhirla 
rrf'sfafa,  the  A.  phmui  of  Liuna'us,  but  is  imicli  elosev  in  lialtit,  tiie 
liydrotliecfB  are  Avider-inouthed  and  shallower  and  the  teeth  upon  tlie 
rim  are  unequal.  An  inipoi-tant  error  occurs  in  the  synonyniv  ol'liiis 
species  given  bj'^  Mr.  A.  Agassiz.  lie  has,  under  the  name  .\<ihio- 
phenia  Franciscana  the  foHowing  synonymy  : 

Plumularai  Franci.'^caiia  Trask. 

Plumularla  struthiontdes  Murray. 

The  Pluriiidarla  Franciscana  of  Trask  l)elongs  to  tlie  geiuis  Jfi/- 
drallmanki:  of  llincks,  as  a  glance  at  the  figures  and  description  of 
Trask  will  show;  and  it  is  synonymous  witli  the  Phnnalarid  gracilis 
of  Murray.  Hence  the  name  of  the  above  descriljed  species  should  not 
be  A.  Franciscana,  but  .1.  strut hionides. 


EXPLANATION  OF  PLATES.    ' 
Plate  XXXVIII. 

Figure  1. — Eudendrium,  s]). ;  from  Santa  Cruz,  Cal. 

Figure  2. — Tubularia  elegans;  a,  cluster  of  medusas  buds;  a,  a',  and«",  buds  in  differ- 
ent stages  of  development ;  a'",  an  actinula  escaping. 
Figure  3. — Bimeria  gracilis ;  a,  a'  and  a",  sporosacs. 
Figure  4. — Sertularella  turgida ;  a,  the  gonangium  or  gonotheea. 
Figure  5. — Sertularella  tur/jida ;  another  form  of  gonotheea. 
Figure  6. — Sertularia  Greenei ;  a.  and  a',  the  gonangia  (gouothecte) ;  h,  hydrotheca. 

Plate  XXXIX. 

Figure  1. —  Campanularia  cylindrica ;  la,  the  same  showing  the  full  length   of  the 

pedicel;   1  fc,  the  female  gonotheea ;   Ic,  an  abnormally  dev^eloped  'lydrotheca ;   \d, 

the  male  gonotheea. 
Figure  2. — Campanularia  Jusiformis ;  '2a,  '2h,  and  2d,  the  same  showing  the  amount  of 

variation  in  the  width  and  depth  of  the  hydrotheca? ;  2e,  2/1  and  2(/.  the  gonothecse ; 

r,  the  rootstock  or  creeping  stem. 
Figure  3. — Sertularia  furcata ;  a,  and  a',  the  gonothecte. 

Figure  4. —  Campamdaria  everta;  a,  and  a',  the  gonotheea?;  r,  the  creeping  stem. 
Figure  5. — H^lecium  tenellum  ;  from  San  Diego,  Cal. ;  r,  the  creeping  stem. 

Plate  XL. 
Figure  1. — Sertularia  anguina;  la,  a  single  hydrotheca  showing  the  outline  of  the 

outer  margin  of  the  rim. 
Figure  2. — Sertularia  anguina;  a  portion  of  the  main  stem. 
Figure  3. — Sertularia  anguina,  var.  rohusta;  a  portion  of  the  main  stem. 
Figure  4. — The  same ;  portion  of  a  branch  ;  a,  gonotheea. 
Figure  5.  — The  same;  with  a  monstrosity,  a.  at  the  extremity  of  the  branch. 


264  ^.  J^l  Clark — Hydroids  of  the  Pacific  Coast. 

Plate  XLI. 
Figure  1. — Plumularia  setacea ;  portion  of  a  branch  with  neinatophores  and  female 

gonothecaj,  a. 
Figure  2. — The  same;   a  portion  of  the  main  stem;  n,  uematophores ;  /;,  hydrothecaj ; 

2a,  male  gonotheca. 
Figure  3. — Aglaophenia  struthionides ;  a  portion  of  a  pinna ;   3a,  36,  and  3c,  different 

views  of  the  same;  n  and  «',  nematophores ;  h,  hydrotheca;  3tZ,  cortaula;  «,  the 

body  of  the  eorbula;  6,   the  wing-like  processes   at   the  base;  n,   and  -«',   the 

nematophores;  /*,  the  hydrothecte. 


VII.  On    the   Anatomy    and    Habits    of    Nereis   virens.      By 
Frederick  M.  Turnbull. 


Read  January  19,  1876.* 


The  Nereis  [Alitta)  virens^  which  is  one  of  the  Largest  and  most 
common  of  our  marine  annellids,  is  found  under  stones  or  burrowing 
in  the  sand  and  mud  of  sheltered  shores,  both  at  low-water  mark, 
and  at  a  considerable  distance  farther  up.  It  grows  to  the  length  of 
eighteen  inches  or  more,  and  is  quite  stout  in  its  proportions. 

It  is  very  active  and  voracious,  feeding  on  other  worms  and  vari- 
ous kinds  of  marine  animals  which  it  finds  when  burrowing  in  the 
sand.f  It  will  even  devour  its  own  immediate  relatives,  if  hungry 
when  it  meets  them.  It  suddenly  thrusts  out  its  proboscis  and 
seizes  its  prey  with  the  two  powerful  jaws,  then  withdraws  the  pro- 
boscis, the  jaws  closing  at  the  same  time.  In  this  way  it 
w'ill  tear  large  pieces  from  the  body  of  its  victim,  being  able,  at 
one  bite,  to  cut  in  two  a  worm  of  its  own  size.  One  which  I  had 
confined  in  a  small  dish  of  water,  bit  its  own  body  in  two  pieces 
at  the  middle.  As  the  proboscis  is  turned  inside  out,  when  it  is  pro- 
truded, whatever  has  been  siez<'d  by  the  jaws  will  be  drawn  by  them 
inside  the  proboscis  as  soon  as  the  latter  resumes  its  natural  jjosition, 
the  proboscis  then  acting  as  a  sort  of  gizzard. 

These  worms,  by  secreting  a  viscid  fluid,  will  surround  themselves 
in  a  few  minutes  with  a  translucent  sheath  which  binds  the  grains  of 
sand  together,  forming  a  loose  and  flexible  tube.  They  remain  most 
of  the  time  in  these  tubes,  Avhich  are  nearly  always  situated  in  sand 
and  mud  or  under  flat  stones,  and  they  move  in  them  with  consider- 

*  Abstract  of  a  graduation  thesis  presented  at  tlie  Sheffield  Scientific  School,  June, 
1875. 

f  Later  observations  show  that  this  species  does  not  restrict  itself  to  an  animal 
diet.  Several  large  specimens,  taken  by  me  in  October,  1875,  had  the  intestine  com- 
pletely filled  witli  algte  of  several  species,  among  which  Ulva  latissima  was  most 
abundant.  The  algas  were  torn  into  fragments  and  large  shreds  and  rolled  together 
into  long  pellets,  but  even  after  passing  through  the  intestine  their  nature  could  be 
easily  recognized. — a.  k.  verrill. 

Trans.  Conn.  Ac.\d.,  Vol.  III.  34  August,  1876. 


266      F.  M.  Turnlmll — Aviatomy  and  Habits  of  JSfereis  virens. 

al)le  freedom  and  rapidity,  pusliiiig  themselves  along  by  means  of 
their  aciculse,  setse  and  ligula^,  the  acicuhe  being  controlled  by 
special  muscles.  They  hold  their  tentacular  cirri  straight  out  in 
front  of  them,  as  they  move,  in  order  to  have  warning  of  anything 
that  they  may  approach. 

The  tautog,  scnp  and  other  fishes  dig  them  out  of  the  sand  and 
devour  them  eagerly.  But  at  certain  times,  especially  at  night,  they 
leave  their  burrows,  and  swim  about  like  eels  or  snakes,  in  large  num- 
bers, and  at  such  times  fall  an  easy  prey  to  many  kinds  of  fishes. 
This  habit  seems  to  be  connected  with  the  season  of  reproduction. 
They  were  thus  observed  swimming  at  the  surface  in  the  day  time, 
near  Newport,  in  April,  1 872,  by  Mr.  T.  M.  Prudden  and  Mr.  T.  H. 
Russell,  and  several  times  by  Professor  Verrill,  later  in  the  season. 
At  Watch  Hill,  R.  I.,  April  12th,  1873,  Professor  Verrill  found  great 
niimbers  of  the  males  swimming  in  the  pools  among  the  rocks  at  low- 
water,  and  discharging  their  milt.  The  males  were  also  seen  swim- 
ming in  the  tide-pools  and  shallow  waters  at  Savin  Rock,  April,  1875, 
by  Professor  D.  C  Eaton  and  Mr.  Kleeberger.  The  JVereis  virens  is 
abundant  at  all  seasons  of  the  year,  in  most  places  along  the  sandy 
and  muddy  shores,  both  of  the  sounds  and  estuaries,  burrowing  near 
low-water  mark.  It  occurs  all  along  the  coast,  from  New  York  to 
the  Arctic  Ocean,  and  is  also  found  on  the  northern  coasts  of  Europe.* 

The  body  consists  of  a  large  number  of  rings  or  segments.  This 
number  varies  with  the  size  and  age  of  the  worm.  It  may  be  less  than 
one  hundred,  or  as  many  as  two  hundred.  The  increase  in  length 
takes  place  by  the  addition  of  new  posterior  segments,  in  advance  of 
the  caudal  segment.  New  segments  may  also  be  formed  when  a  part 
of  the  body  is  broken  oif,  and  in  this  way  a  considerable  part  of  the 
posterior  portion  of  the  body  can  be  completely  reproduced.  The  head 
(figs.  1  and  17)  is  very  fully  developed,  being  provided  with  two 
pairs  of  eyes  and  two  pairs  of  antennae.  It  is  attached  to  the  dorsal 
side  of  the  first  segment,  wliich  is  called  the  buccal  or  mouth-ring 
(figs.  1  and  15,  d),  because  it  contains  the  mouth  (fig.  15,  ni).  There 
are  also  four  feelers,  called  tentacular  cini  (fig.  1,  ee,  ee',  e  and  e'), 
arising  from  the  buccal  ring  on  each  side  of  the  head. 

The  abdominal  rings  (fig.  1,  g)  follow  the  buccal  ring.  Each  one 
of  these  has  a  pair  of  lateral  lamelliform  appendages  (figs.  1  and  1  7,  A), 
used  as  paddles  in  swimming  and  also  Serving  the  purpose  of  gills. 
The  last  segment  or  ring  of  the  body  bears  a  pair  of  cirri,  similar  to 
the  tentacular  cirri,  and  also  contains  the  anal  orifice. 

*  See,  for  habits  of  this  and  allied  species,  Professor  VerriU's  report  in  First  Report 
of  U.  S.  Commission  of  Pish  and  Fisheries,  p.  318.     1873. 


F.  M.  Turnhidl — Anatomy  and  Hahits  of  Nereis  virens.      267 

The  mules  are  easily  distinguished  from  the  females  by  ditferences 
in  color  and  in  the  form  of  the  side  appendages.  The  color  of  the 
body  in  the  male  is  an  intense  steel-blue,  which  blends  into  green  at 
the  base  of  the  lateral  appendages.  These  have  a  rich  and  brilliant 
sea-green  color  which  is  heightened  by  the  complimentary  effect  of 
the  luimerous  red  blood-vessels  they  contain.  The  latter  are  especially 
noticeable  toward  the  posterior  end  of  the  body  where  the  skin  is 
thinner  and  less  opaque,  so  that  the  appendages,  with  their  network 
of  ca|»illaries,  appear  bright  red. 

In  the  female  the  body  is  of  a  dull  greenish  color,  with  a  slight  tinge 
of  orange  and  red.  The  appendages  are  orange-green  at  the  base, 
and  become  bright  orange  toward  their  extremities ;  but  sometimes 
they  are  greenish  throughout.  The  whole  surface  of  the  skin,  in  both 
male  and  female,  is  iridescent,  reflecting  bright  hues  when  placed  in 
the  light. 

The  head  (figs.  1  and  15,  a)  is  small,  and  flattened  on  the  doisal  and 
ventral  sides.  From  the  position  of  the  anterior  eyes  the  sides  taper 
toward  the  anterior  extremity,  where  it  is  rounded  oft'  and  terminated 
by  a  pair  of  small  antenna  (figs.  1  and  15,  h,  b).  There  are  two  pairs 
of  eyes  on  the  upper  surface  of  the  head,  one  pair  near  its  base  and 
another  pair  more  anterior  and  farther  apart.  The  anterior  eyes  are 
situated  near  the  middle  and  on  the  broadest  portion  of  the  head. 
On  each  side  of  the  head,  attached  to  its  anterior  half  and  also  to  the 
buccal  ring,  is  a  large  antenna  or  palpus,  as  it  is  sometimes  called  (figs. 
1  and  15,  c).  These  are  stout,  fleshy  and  somewhat  contractile  organs. 
Each  has  a  small  rounded  lobe  at  the  tip  (figs.  1  and  15,  c'). 

The  buccal  segment  and  the  head  constitute  the  cephalic  or  head 
region.  The  tegument  about  the  mouth  is  wrinkled  and  folded  lon- 
gitudinally, presenting  an  appearance  like  the  mouth  of  a  purse,  when 
drawn  together  by  strings.  The  tentacular  cirri  are  long,  slender 
and  quite  flexible.  They  receive  their  nerves  from  the  first  abdominal 
nerve-ganglion,  whereas  the  antennae  receive  theirs  from  the  head- 
ganglion. 

There  are  four  pairs  of  tentacular  cirri,  two  dorsal  (fig.  1 ,  ee,  ee')  and 
two  ventral  (fig.  1,  e,  e').  The  ventral  ones  are  situated  nearer  to  the 
palpi  than  the  doi'sal,  and  hence  the  two  are  called  respectively  the 
internal  and  external  tentacular  cirri.  The  relative  lengths  of  the  ten- 
tacular cirri  are  shown  in  fig.  1.  The  two  large  dorsal  tentacular  cirri 
(ee,  ee)  are  longer  in  the  male  than  in  the  female.  In  the  male  they 
will  reach  to  about  the  middle  of  the  ninth  segment,  when  laid  along 
the  back.     In  the  female  they  will  reach  to  about  the  middle  of  the 


268      F.  M.  Turnhull — Anatomy  and  Habits  of  Nereis  virens. 

fifth  segment.  The  other  tentacular  cirri  have  more  nearly  the  same 
length  in  both  sexes. 

The  abdominal  segments  increase  in  size  to  about  the  eighth,  and 
then  remain  nearly  the  same  for  some  distance  along  the  middle 
region,  but  the  posterior  rings  decrease  in  size,  causing  the  body  to 
taper  until  it  becomes  quite  slender.  The  appendages,  also,  are  longer 
and  broader  along  the  middle  region  than  toward  either  extremity. 
On  the  ventral  side  of  the  segments  the  part  continuous  with  the  feet 
is  smooth,  l)ut  the  other  parts  show  the  strong  transverse  muscles 
(fig.  26),  which,  by  their  contraction,  lessen  the  size  of  the  body  cavity. 

The  lateral  appendages  or  feet  of  Nereis  virens  are  quite  compli- 
cated and  wonderful  organs.  They  are  biramous  (fig,  12),  having 
two  rami,  one  dorsal  (A)  and  the  other  ventral  (B).  The  aciculse  of 
each  foot  arise  from  a  crypt  which  is  attached  by  shroud-like  muscles 
to  the  base  of  the  foot.  The  sette  arise  from  the  interior  of  the 
two  rami.  The  feet  are  complicated  by  the  addition  of  other  organs, 
serving  for  locomotion,  sensation  and  respiration. 

The  respiratory  organs,  often  called  liguhne,  are  moi-e  or  less  flatten- 
ed lobes  with  their  teguments  very  thin  and  filled  \\\i\\  a  rich  vascu- 
lar netw'ork  (figs.  22,  s^  25,  26).  The  upper  ramus  has  two  ligulae,  a 
superior  one  (fig.  12,  h)  on  its  upper,  and  an  inferior  one  (fig.  12,  d)  on 
its  lower  side.  At  the  base  of  the  superior  ligula,  on  a  sort  of  shoulder 
of  its  upper  edge,  is  the  dorsal  cirrus  (fig.  12,  a).  There  are  also  two 
setigerous  lobes  smaller  than  the  liguhe,  one  on  each  side  of  the  open- 
ing through  which  the  sette  protrude  (fig.  12,  c  and  k).  The  anterior 
(c)  is  longer  than  the  other  [k)  and  is  connected  with  the  inferior  ligula 
{d)  of  the  upper  ramus.  The  acicula  is  attached  to  the  inner  walls 
of  the  ramus  forming  a  partition,  which  terminates  with  the  end  of 
the  acicula  between  the  lolies  c  and  d,  (fig.  12)  and  generally  forms, 
in  the  middle  and  posterior  parts  of  the  body,  a  third  and  smaller  lobe 
(fig.  12,  r'). 

The  lower  i-anius  lacks  a  superior  ligula,  but  it  has  an  inferior  one 
(fig.  12,^)  more  rounded  and  not  so  broad  as  the  others.  In  the  lower 
ramus,  as  in  the  upper,  there  is  normally  only  one  fascicle  of  setae, 
but  in  the  lower  ramus  it  is  divided  into  two  clusters  by  the  acicula, 
which,  by  its  attachment  to  the  inner  walls  of  the  ramus,  forms  a  par- 
tition. Here,  as  in  the  u])per  ramus,  there  are  two  flattened  setiger- 
ous lobes,  about  equal  in  length,  one  on  each  side  of  the  o])ening  for 
the  setae  (fig.  12,  /  and  e),  and  the  partition  formed  by  the  acicula 
extends  to  the  extremity  of  the  anterior  one,  dividing  it  into  two  small 
lobes  (fig.  12,  e  and  e). 


p.  M.  Turiihidl — Anatomy  (otd  Ilahits  of  Nereis  vlrois.      '269 

The  inferior  ligiihi  of  the  u])per  nuiius,  with  its  two  hjhes  (tig.  12, 
c,  d)  corresponds,  apparently  to  the  lobe  (e)  and  its  divisions,  while 
the  lobe  {k)  of  the  upper  ramus  corresponds  to  the  lobe  (/)  of  the 
lower  ramus.  In  the  upper  ramus,  the  acicula  and  its  partition  do 
not  divide  the  bunch  of  setae,  as  it  coAies  out  above  the  acicula. 
The  ventral  cirrus  arises  from  a  slight  protuberance  of  the  inferior 
side  of  the  lower  ramus  (fig.  12,  h). 

The  feet  are  not  all  alike  from  one  end  of  the  body  to  the  other ; 
they  change  in  form  most  along  the  anterior  region,  and  in  the  first 
five  the  variation  is  considerable ;  along  the  middle  and  posterior 
regions,  it  is  slight  in  comparison, 

I  have  figured  tlu'  first  five,  the  forty-fifth,  and  the  one  hundred-and- 
ninth  feet  of  a  female  worm,  having  one  hundred  and  twenty-one 
segments;  also  the  first,  fifth,  forty-fifth,  and  one  hundred-and-ninth  in 
a  male  worm  of  nearly  equal  size,  but  having  one  hundred  and  sixty- 
one  segments.  These  figures  show  the  posterior  view  of  the  feet. 
Those  of  the  female  will  be  first  described,  and  then  compared  with 
those  of  the  male. 

In  the  first  foot  of  the  female  (fig.  3)  the  upper  ramus  has  only  the 
doi'sal  cirrus  and  the  superior  ligula  developed.  The  former  is  about 
one-fifth  longer  and  a  little  less  than  one-third  as  broad  as  the  latter, 
being  very  well  dcA^eloped,  wdiile  the  ligula  is  somewhat  rudimentary. 
The  ligula  is  rounded  and  simple  in  shape,  having  a  constriction  at  its 
base.  Of  the  lower  ramus,  all  the  parts  are  present.  The  posterior 
setigerous  lobe  (/')  is  longer  than  the  anterior  setigerous  lobe  (e),  and 
is  oval  and  flattened.  The  anterior  setigerous  lobe  {e)  is  seen  to  be 
divided  by  the  acicula  into  two  smaller  terminal  lobes  (e  and  e'),  in- 
dicated by  dotted  lines  where  they  are  covered  by  the  posterior  seti- 
gerous lobe  (/").  The  inferior  ligula  {g),  of  the  lower  ramus,  is  of 
about  the  same  size  and  shape  as  the  superior  ligula  [h],  and  the  infe- 
rior cirrus  (//),  is  like  the  superior  cirrus  {<().  The  setse  of  the  lower 
ramus,  as  shown  in  the  figure,  extend  just  Ijeyond  the  posterior  seti- 
gerous lobe  (/').  They  are  somewhat  rudimentary  and  are  for  the 
most  part  blunt.     The  acicula  is  also  rather  small. 

The  second  foot  (fig.  4)  has  the  anterior  setigerous  lobe  (e),  and  the 
acicula  a  little  larger  and  better  developed,  and  the  dorsal  cirrus  is 
seen  to  be  a  little  shorter  than  that  of  the  first  foot;  otherwise  the 
second  foot  is  scarcely  different  from  the  first. 

In  the  third  foot  (fig.  5)  the  upper  ramus  has  developed  an  inferior 
ligula,  setjB  and  acicula.  It  also  has  an  anterior  setigerous  lobe 
(c).     This  lobe  is  a  part  of  the  inferior  ligula  [d).     It  shows  more 


210      F.  M.  Tumhidl — Anatomy  and  Habits  of  Nereis  virens. 

distinctly  in  some  of  my  figures  of  the  feet  of  the  male.  The  superior 
ligula  is  of  about  the  same  size  and  shape  as  the  inferior  ligula.  The 
lower  ramus  is  a  little  more  developed  than  it  is  in  either  the  first  or 
second  feet,  but  the  inferior  cirrus  (A)  is  shorter. 

The  fourth  foot  (fig.  6)  is  more  highly  developed  than  the  third  ; 
but  the  inferior  cirrus  is  shorter  in  comparison  with  the  lower  ramus. 

The  fifth  foot  (fig.  7)  is  still  more  highly  developed  than  the  fourth, 
and  the  superior  ligula  is  larger  than  it  is  in  the  preceding  feet.  The 
dorsal  and  ventral  cirri  are  both  smaller.  If  we  now  compare  the  fig- 
ure of  the  fifth  with  the  figures  of  the  first  and  second  feet,  the  differ- 
ence is  seen  to  be  considerable,  particularly  in  the  length  of  the  cirri. 

The  superior  ligula  {b)  begins  to  increase  in  size  at  the  fifth  foot, 
and  continues  to  do  so,  until  in  the  forty  fifth  (fig.  8,  h)  it  is 
larger  than  any  other  part  of  the  foot.  It  has  also  become  flat 
and  pointed.  The  shoulder  (?")  is  much  larger.  The  inferior  ligula 
[d)  is  also  flat  and  pointed.  A  posterior  setigerous  lobe  {k)  is  now 
large  enough  to  be  easily  seen.  The  posterior  setigerous  lobe  (/)  of 
the  lower  ramus  is  somewhat  pointed,  and  its  lower  edge  is  oblique. 
The  anterior  setigerous  lobe  (e)  is  now  as  long  as  the  posterior  seti- 
gerous lobe,  and  its  two  divisions  are  nearly  equally  developed.  The 
inferior  ligula  {g)  is  rounded  and  somewhat  tapering  toward  its 
extremity.  The  dorsal  and  venti'al  cirri  are  now  quite  small,  particu- 
larly the  latter,  while  otherwise  the  foot  is  much  larger.  The  setse 
have  become  longer  and  more  perfect,  from  the  anterior  toward  the 
posterior,  attaining  their  maximum  in  the  middle  region  of  the  body. 
The  aciculiB  are  also  larger  here  than  in  either  the  anterior  or  pos- 
terior regions ;  although,  in  the  posterior  region  they  are  longer  in 
comparison  with  the  size  of  the  foot  than  anywhere  else. 

The  one  hundred  and  ninth  foot  (fig.  9),  as  shown  by  the  figures,  is 
nearly  the  same  in  form  as  the  forty-fifth,  but  smaller. 

On  comparing  the  first,  fifth,  forty-fifth  and  hundred  and  ninth 
feet  of  the  female  with  the  same  in  the  male,  we  find  that  there  is  a 
marked  difference  in  the  cirri.  The  dorsal  cirrus  in  the  first  foot  of 
the  male  (fig.  10)  is  one-half  longer  than  it  is  in  the  female,  and  it  is 
larger  in  proportion.  In  the  fifth  foot  (fig.  1 1 )  the  difference  is  the 
same.  In  the  forty-fifth  (fig.  12)  the  dorsal  cirrus  of  the  male  is  longer 
and  also  slenderer  than  it  is  in  the  female.  In  the  one  hundred  and 
ninth  foot  (fig.  13)  the  dorsal  cirri  are  about  the  same  in  length,  but 
those  of  the  male  are  more  slender. 

The  difference  between  the  dorsal  cim  decreases  toward  the  posterior 
end  of  the  bodi/,  being  greatest  in  the  anterior  segments. 


F.  M.  Turnhnll — Anatomy  and  Habits  of  ]Vereis  virens.      271 

The  ventral  cirrus  of  the  first  foot  of  the  raale  (tig,  10)  is  not  quite 
so  long  as  the  dorsal  cirrus,  but  it  is  a  little  longer  than  the  venti'al 
cirrus  of  the  female.  In  the  fifth  foot  (fig.  11)  it  is  a  little  longer  and 
much  more  slender  than  it  is  in  the  female.  In  the  forty-fifth  (fig.  12) 
it  is  twice  as  long  and  of  the  same  diameter  as  it  is  in  the  female. 
In  the  one  hundred  and  ninth  (fig.  13)  there  is  the  same  difference 
which  we  see  in  the  foi'ty-fifth. 

The  difference  between  the  ventral  cirri  of  the  male  and  female,  in- 
creases from  anterior  to  ^yosterior,  being  greatest  m  the  posterior  seg- 
ments. 

Beginning  with  the  forty-fifth  foot  (fig.  12)  a  shoulder  {x)  appears  on 
the  dorsal  side  of  the  lower  ramus  in  the  male.  It  increases  in  size  and 
definiteness  farther  back,  but  finally  disappears.  This  shoulder 
is  never  seen  in  the  female,  and  is  a  good  character  for  distinguishing 
the  sexes,  but  it  requires  microscopic  examination.  The  difterence 
between  the  cirri  of  the  male  and  female  is  suflicient  to  distinguish 
them  without  the  use  of  a  lens. 

The  setae  under  the  microscope  are  very  delicate  and  beautiful  (figs. 
2.  la).  They  consist  of  two  parts,  the  shaft  (a)  and  the  blade  (J). 
The  shaft  has  a  transversely  striated  appearance,  which  is  exceedingly 
regular.  The  blade  is  held  in  a  sort  of  socket  in  the  end  of  the  shaft, 
and  one  edge  is  toothed  like  a  saw.  There  are  two  forms :  one  in 
which  the  blade  is  short,  having  its  extremity  blunt  and  slightly 
hooked  (fig.  2),  and  one  with  the  blade  tapering  to  a  fine  point, 
the  blade  being  long  and  slender  (fig.  2a).  The  length  varies  and 
with  it  the  delicacy  of  the  point.  In  most  of  the  setae  the  latter  is 
so  sharp  that  it  seems  to  vanish,  and  can  be  seen  only  with  a  high 
power.  Those  setse  which  are  hooked  have  the  hooks  and  toothed 
edge  turned  upward;  and  these  are  always  confined  to  the  lower 
ramus,  and  to  the  lower  side  of  the  latter  in  both  bunches.  In  the 
middle  and  posterior  regions  these  hooked  setae  disappear,  their  place 
being  taken  by  the  other  kind ;  but  the  latter  are  shorter  than  those  in 
the  upper  part  of  the  bunch.  The  same  forms  of  seta?  are  found  in 
both  male  and  female.  Those  of  the  anterior  feet  are  shorter  than 
those  in  the  middle  region.  When  viewed  by  transmitted  light  the 
bunches  present  all  the  colors  of  the  spectrum. 

The  aciculge  (figs.  12  and  22)  are  simple  thorns,  in  the  form  of  an 
elongated  cone,  generally  a  little  bent.  They  are  black,  except  at  the 
base,  showing  through  the  translucent  integuments  of  the  foot.  At 
the  base  they  are  hollow  and  therefore  lighter  colored. 


272      F.  M.  Turnhull — Anatomy  and  Habits  of  JSTereis  virens. 

Muscular  System. 

The  walls  of  the  body  contain  two  muscular  layers,  which  are 
well  defined.  The  first  is  thick  on  the  ventral  side  of  the  body 
(fig.  22,  k),  but  is  thinner  elsewhere.  It  forms  in  each  ring  a  muscular 
plane  of  transverse  fibres.  The  second  is  placed  within  the  jjreceding 
and  is  formed  of  great  fascia?  which  are  attached  to  the  interannuiar 
partitions  (fig.  16,  b).  This  layer  does  not  exist  on  the  ventral  side, 
between  the  bases  of  the  feet.  The  interannuiar  partitions  (fig.  16,  a) 
are  attached  to  the  intestine,  which  they  hold  in  place,  dividing  the 
general  cavity  of  the  body  into  a  series  of  chambers  (fig.  16) ;  but  as 
the  inner  subcutaneous  layer  does  not  extend  over  the  ventral  floor 
of  the  cavity,  the  chambers  open  into  one  another  beneath  the  intes- 
tine. I  have  already  mentioned  the  muscles  attached  to  the  fleshy 
knobs,  which  hold  the  aciculfe.  These  muscles  (fig.  22),  when  they 
contract  all  together,  force  the  aciculae  outward.  When  difterent  ones 
contract  they  move  the  aciculffi  to  one  side. 

The  Nereis  virens  in  swimming  moves  its  body  laterally,  like  a 
snake.  It  sometimes  has  also  an  undulatory  movement,  up  and  down. 
These  motions  are  all  produced  by  the  subcutaneous  miiscles.  The 
lateral  appendages  are  used  as  paddles,  but  their  principal  use  is  to 
push  the  worm  along  in  its  tube,  and  for  crawling.  They  are  greatly 
aided  by  the  stifle  aciculffi,  controlled  by  their  special  muscles  (fig. 
22),  and  by  the  seta\  When  burrowing,  the  proboscis  is  used  to  push 
away  the  sand  in  front  and  is  then  withdrawn,  while  the  body  is  moved 
forward  partly  by  a  vermicular  motion  and  partly  by  the  side  ap- 
pendages. 

Alimentary  Syste)n. 

The  proboscis  is  a  very  remarkable  organ  and  constitutes  a  formid- 
able weapon.  It  is  divided  by  M.  DeQuatrefages  into  three  regions: 
the  pharyngeal,  the  dental,  and  the  oesophageal  (figs.  16-18).  The 
mouth  has  already  been  partially  described.  The  walls  of  its  cavity 
are  connected  by  several  small,  delicate  muscles,  with  the  walls  of  the 
body  cavity,  as  I  have  shown  in  figure  16,  m  and  n.  The  pharyngeal 
region  commences  immediately  back  of  the  buccal  cavity  (figs.  16  and 
20,  x),  and  has  two  muscular  partitions  (fig.  16,  c). 

The  dental  region  (20  and  16,  jo)  is  very  muscular,  and  is  provided 
with  a  considerable  number  of  small  teeth,  or  denticles,  which  are 
arranged  in  groups  on  the  anterior,  inner  surface  of  its  walls.  It  also 
has  two  large  and  powerful  jaws  attached  by  their  hollow  bases  to  the 
muscles  of  the  posterior  inner  surface.  The  worm  has  the  power  of 
turning  this  dental  region  inside  out. 


F.  M.  Turnhull — Anatomy  and  Habits  of  Nereis  virens;.      273 

Whoii  the  proboscis  is  iiisido  the  body,  it  takes  the  position  sliown 
in  tiniires  16  and  20,  tlie  cesojthagus  being  curved  and  pushed  back 
against  the  intestine ;  but  when  it  is  forced  out,  the  oesophagus 
straightens,  and  that  part  of  the  proboscis  which  is  protruded  takes 
the  position  shown  in  figures  1  7  and  1 8,  these  figures  sliowing  the  ar- 
rangement of  the  jaws  and  denticles,  figure  17  giving  the  dorsal 
view  and  figure  18  the  ventral  view;  the  buccal  ring  is  very  much 
stretched  ;  and  the  head,  antenna^  and  tentacular  cirri  are  forced  over 
on  the  back  (fig.  17).  The  jaws  are  imbedded  in  and  attached  to 
the  special  muscles,  in  such  a  manner  that  the  more  the  proboscis  is 
l^rotrudcd  the  farther  apart  their  points  move,  and  when  the  probos- 
cis is  withdrawn  they  close  like  a  pair  of  scissors,  their  points  crossing. 
The  jaws  (fig.  19)  are  curved  like  hooks,  and  have  their  inner  concave 
edge  denticulated  with  about  ten  teeth.  They  and  the  denticles  are 
composed  of  a  black  chitinous  material.  The  denticles,  which  are 
conical  and  pointed,  are  not  attached  to  muscles,  but  are  simply  im- 
bedded in  the  surface.  The  number  and  size- of  the  denticles,  and 
even  their  positions,  vary  considerably  in  the  different  specimens  ex- 
amined. T  think  it  would  be  hard  to  fi.nd  two  specimens  exactly  alike 
in  this  respect.  Among  seven  worms,  I  found  five  with  one  denticle, 
one  with  two  denticles,  and  one  with  seven  denticles  on  the  median 
anterior  area  of  the  dorsal  side  (fig.  17,  o). 

Among  six  worms,  I  found  two  with  two  denticles  and  four  with 
none  at  all  on  the  posterior  median  area  of  the  dorsal  side  (fig.  17,  t). 
On  the  left  submedian  anterior  area  of  the  dorsal  side  (fig.  17,  I),  the 
number  of  denticles  varied  from  three  to  eight ;  and  on  the  right  sub- 
median  anterior  area  of  the  dorsal  side  (fi:g.  17,  I')  from  two  to  eight. 
In  only  one  case  did  the  two  last  areas  have  the  same  number  of  den- 
ticles.    On  the   left  submedian  posterior  area  of  the  dorsal  side  (fig. 

17,  s)  the  number  of  denticles  varied  from  none  to  five;  and  on  the 
light  submedian  posterior  area  of  the  dorsal  side  (fig.  1 7,  s')  from 
one  to  four. 

The  denticles  on  the  lateral  and  ventral  posterior  areas  (fig.  17  and 

18,  r)  vai-y  considerably  in  number,  position  and  size.  Among  four 
worms,  the  number  of  denticles  on  the  right  lateral  anterior  area  (figs. 
17  and  18,  n)  varied  from  twelve  to  twenty-five;  and  on  the  left  lat- 
eral anterior  area  (figs.  17  and  18,  n')  from  eleven  to  thirty. 

Among  five  worms  the  number  of  denticles  on  the  anterior  median 
area  of  the  ventral  side  (fig.  18,  y)  varied  from  four  to  twelve.  On 
each  of  the  two  submedian  *  areas  of  the  ventral  side  (fig.  18,  x') 
there  was  one  denticle. 

Trans.  Conn.  Acad.,  Vol.  III.  35  August,  1876. 


274      F.  31.  Tarnhull— Anatomy  and  Habits  of  Nereis  virens. 

In  some  of  the  large  worms  the  denticles  are  as  small  as  those  of 
smaller  worms,  while  in  other  cases  they  are  much  larger.  The  large 
denticles  probahly  are  knocked  off  in  some  way  and  new  ones  grow 
in  their  place.  This  would  account  in  part  for  the  large  number  of 
very  small  denticles,  and  also  for  the  variations  in  number. 

Attached  to  the  anterior  end  of  the  oesophagus,  one  on  each  side, 
are  two  salivary  glands  (figs.  IH  and  20,  j).  These  are  free  except  at 
one  end,  and  are  ciliated  on  their  outer  surface.  The  intestine  proper 
(figs.  16  and  20,  r)  is  straight  and  is  constricted  somewhat  by  the 
muscular  partitions  of  each  segment  through  which  it  passes.  It  is 
brilliant  greenish  yellow  in  color  and  is  surrounded  by  a  regular  cap- 
illary network  of  blood  vessels  (fig.  20). 

The  internal  surface  of  the  oesophagus  is  tessellated  with  low,  rounded 
papillae  or  tubercles,  "^rhese  are  regular  in  shape  and  equal  in  size. 
Their  sides  are  diag<mal  to  the  length  of  the  oesophagus.  They  show 
through  the  walls  of  the  oesophagus,  so  that  its  outside  appears  tessel- 
lated with  dark  squares,  and  as  the  oesophagus  is  stretched  or  con- 
tracted they  become  diamond  shaped.  The  tubercles  are  of  a  dull 
color,  between  brown  and  yellowish  green. 

The  intei'ior  surface  of  the  intestine  is  also  covered  with  regular 
longitudinal  rows  of  low,  rounded  tubercles,  which  are  much  smaller 
than  those  of  the  (esophagus.  They  are  greenish-yellow  like  the  out- 
side of  the  intestine.  The  end  of  the  oesophagus  projects  into  the 
cavity  of  the  intestine,  and  its  opening,  which  has  sphincter  and  also 
longitudinal  muscles,  can  be  enlarged  or  contracted  to  a  considerable 
extent.  The  outer  surface  of  this  end  of  the  oesophagus  is  continuous 
with  and  like  the  internal  surface  of  the  intestine.  The  latter  secretes 
a  brown  fluid  in  its  interior  and  probably  acts  as  a  hepatic  organ. 
The  dental  portion  of  tlie  proboscis  acts  like  a  gizzard,  and  the 
oesophagus  is  pi'obably  a  sort  of  stomach. 

Circulation  and  Respiration. 

The  circulatory  system  is  highly  developed  and  complicated.  The 
blood  is  red,  and  the  vascular  system  is  complete  and  closed.  The 
principal  vessels  have  a  longitudinal  course,  occupying  the  whole 
length  of  the  median  line  of  the  l)ody,  one  as  a  dorsal  (figs.  20- 
24,  a),  and  the  other  as  a  ventral  vessel  (Ji).  They  are  contractile,  and 
by  a  sort  of  peristaltic  motion  the  blood  is  pushed  forward  in  the 
dorsal  vessel,  and  in  the  op])osite  direction  by  the  ventral  vessel. 
The  dorsal  vessel  is  visible  for  nearly  its  whole  length  thi'ough  the 
more  or  less  transparent  walls  of  the  body,  and  its  blood  can  be  seen 


F.  M.  7)(r/)bi«U — Anotomy  <in<]  Ilahits  of  N'erels  virens.      275 

moving  in  a  series  of  waves  toward   the   liead.      The  ventral  vessel 
sends  oif,  in  each  segment  of  the  body,  except  a  few  in  the  region  of 
the  proboscis,  two  smaller  vessels,  one  on  each  side.     These  two  ves- 
sels fork,  each  sending  a  branch  to  the  inferior  ramus  of  the  foot  of 
the  next   segment  to  the  rear  (tigs.   20-24,  /"),   and  another   larger 
branch  ic)  around  the  intestine,  by  the  side  of  the  transverse  parti- 
tion, to  the  dorsal  vessel,  receiving,  also,  on  its  vvay,  a  vessel  from 
the  upper  ramus  of  the  foot  of  its  own  segment  {d).     Jiesides  these 
principal  lateral  vessels,  there  are  five  other  vessels  on  each  side  in 
each  segment,  coming  from  the  ventral  vessel  (iig.  20).   These  form 
a    loose   but    regular   network   that  surrounds   the   intestine    and    is 
connected  with  live  other  convoluted  vessels,  which  join  the  dorsal 
vessel.      This  network  on  the  intestine  probably  supplies  the  hepatic 
organ   with  material  for  its   secretion,  and  very  likely  may  receive 
nutritive    material  from   the   digested   food.     The   blood   moves   in 
waves,  at  regular  intervals,  through  the  peripheral  vessels  (figs.  20- 
24,  c)  to  the  dorsal  vessel,  but  I  could  not  see  in  which  direction  the 
blood  moved  in  the  network.     The  blood  is  forced  into  it  at  each  pul- 
sation of  the  dorsal  vessel,  l)ut  the  normal  flow  may  be  in  the  opposite 
direction.    The  peiipheral  vessels  are  also  connected  with  this  network 
(tig.  20).    The  dorsal  and  ventral  vessels  are  connected  at  the  posterior 
extremity  of  the  body  by  a  simple  peripheral  vascular  ring  (fig.  23,  c), 
in  which  the  blood  flows  from  the  ventral  to  the  dorsal  vessel.     In 
the  region  of  the  proboscis,  the  ventral  vessel  sends  lateral  branches 
directly  to  all  the  feet  but  the  first  three  (figs.  20  and  21).     It  then 
sends  a  pair  of  vessels  to  the  oesophagus  (figs.  20  and  21,  e),  which 
pass  back  along  the  oesophagus,  one  on  each  side,  as  far  as  the  intestine, 
being  connected  with  smaller  vessels  on  the  surface  of  the  oesophagus. 
The  ventral  vessel  next  sends  otf  a  pair  of  vessels  which  expand  into 
capillary  networks,  one  on  each  side  (figs.  20,  21,  s  and  g).     Each  of 
these  networks   sends  small  branches  to  the  first  three  feet  on  its 
own  side,  and  then  merges  into  a  vessel  (figs.  20  and  21,  A),  which 
goes  to  the  base  of  the  tentacular  cirri.     The  ventral  vessel  now  goes 
upward  to  the  under  surface  of  the  proboscis,  and  there  divides  into 
three  branches  (figs.  20,  21,  t,  t  and  /).     The  middle  branch  (fig.  21, 1) 
passes  under  a  muscle  and  along  the  median  line  of  the  ventral  sur- 
face, as  tar  as  the  pharynx,  where  it  divides  into  two,  forming  a  small 
vascular  ring  (fig.  21,  n)  about  the  latter.     The  two  lateral  branches 
pass    upward   and    backward    on    the    proboscis,    each    expanding 
into   a  remarkably  rich  and  delicate  network  on  its  own  side  of  the 
proboscis  (figs.  20  and  21 ,  u).     From  each  of  these  networks  a  vessel 


276      F.  M.  Turnbull — .hiatomy  and  Mabits  of  Nereis  vireus. 

(?;)  passes  to  the  base  of  the  head,  where  it  joins  tlie  dorsal  vessel 
(«),  thus  completing  the  circulation.  From  tliis  junction  small 
vessels  probably  go  into  the  head  and  antennae.  The  lateral  vessel 
passing  to  the  lower  ramus  divides  into  branches  ramifying  on  that 
portion  which  is  continuous  with  the  foot  on  the  ventral  side  of  the 
segment,  and  also  over  the  lower  ramus  (tigs.  22  and  26).  There  a 
connection  is  made  with  vessels  of  the  upper  ramus,  and  I  think 
this  is  done  by  the  vessel  marked  x  in  figures  22  and  24,  because  it  is 
quite  large  at  the  base  of  the  inferior  ligula  of  the  upper  ramus,  and 
grows  smaller  at  first  and  then  swells  out  again  before  joining  the 
vessels  of  the  iipper  ramus,  in  the  superior  ligula.  The  branch  d 
(figs.  20,  22  and  24),  coming  from  the  dorsal  ramus,  receives  blood 
from  that  organ  and  also  from  a  peculiar  and  beautiful  arrangement 
of  capillaries  on  the  dorsal  side  of  the  body  (fig.  25). 

In  the  first  four  segments,  in  the  region  of  the  proboscis,  the  dorsal 
vessel  has  no  branches,  but  in  the  remaining  segments,  commencing 
with  the  fifth,  it  has  five  pairs  of  long  peripheral  branches  (fig,  20,  e,  c'), 
corresponding  to  the  peripheral  vessels  of  the  posterior  part  of  the 
body.  They  are  not  attached  to  the  proboscis,  but  are  simply  con- 
nected with  the  dorsal  and  ventral  vessels  by  their  ends.  The  one 
coming  from  the  dorsal  vessel  in  the  fifth  segment  is  connected  with 
the  ventral  vessel  in  the  fourth  segment  (fig.  20.)  The  first  three 
feet  probably  do  not  act  as  gills,  as  very  little  blood  is  sent  to  them. 
The  two  networks  (figs.  20  and  21,  u)  on  the  proboscis  are  probably 
for  carrying  on  the  exchange  between  the  blood  and  the  liquid  of  the 
body  cavity. 

The  respiration  is  carried  on  by  the  red  fluid  in  the  beautiful  ar- 
rangement of  capillaries  on  the  body  and  feet,  especially  the  latter. 
The  flat  ligulie  of  the  feet  are  exceedingly  delicate  in  structure  and 
take  the  place  of  gills,  absorbing  the  oxygen  from  the  water  to  purify 
the  blood  received  from  the  ventral  vessel,  which  then  returns  to  the 
dorsal  vessel. 

The  disposition  of  this  respiratory  arrangement  is  shown  in  figures 
22,  24,  25  and  26. 

Tlie  Nervous  System.  

^  If  Tuw  - 

The  nervous  system  of  Nereis  vi7^ens  {Ggs.  27  and  28)  is  complicated 

and  well  developed,  being  composed  of  a  series  of  ganglia,  sending 

out  branches  and  connected  by  nervous  cords.     It  lies  mainly  on  the 

ventral  floor  of  the  body  beneath  the  large  ventral  vessel.     The  first 

and  largest  ganglion  (figs,   27   and  28,  a),  analogous  to  the  brain  of 

higher  animals,  is  situated  in  the  head.     It  is  composed  of  several 


KM.  TvrnhnU — Anatomy  and  Habits  of  Nereis  vlrens.       277 

smaller  ganglia  joined  together.  It  bears  tlie  eyes,  on  fo\ir  short  ner- 
vous peduncles,  on  its  dorsal  side.  In  front  it  sends  four  nerves  to  the 
antennje  (/>,  b  and  c,  c,  iigs.  27  and  28).  Laterally  it  sends  out 
two  branches  called  the  connectives  [d,  d),  which  pass  around 
the  mouth  and  proboscis  to  join  the  first  of  the  abdominal  gan- 
glia (A,  tig.  27).  Near  the  junction  of  the  connective  with  the 
head  ganglion,  is  a  small  ganglion  sending  nerves  to  the  internal 
tentacular  cirri  (e,  e,  figs.  27  and  28).  The  connectives,  near  their 
lower  extremity,  send  two  nerves  {g,  g,  fig.  27)  to  a  series  of  ganglia 
and  nerves  on  the  ventral  side  of  the  proboscis  {to,  w,  fig.  27).  There 
is  also  an  accessory  connective  (figs.  27  and  28,  d')  on  each  side,  })ass- 
ing  from  the  first  abdominal  ganglion  to  the  ganglion  supplying  the 
external  tentacular  cirri  {e',e',  figs.  27  and  28).  This  accessory  connec- 
tive also  has  a  ganglion  {ii\  fig.  27)  at  the  middle,  sending  nerves  to 
the  muscular  partitions  of  the  proboscis. 

Each  of  the  first  three  abdominal  ganglia  sends, from  its  anterior  por- 
tion, on  each  side,  a  nerve  that  forks,  one  branch  (fig.  27,  n)  going  to  the 
muscular  partition  and  the  other  (o)  passing  through  the  partition  to 
the  preceding  segment.  In  the  remaining  abdominal  ganglia,  begin- 
ning with  the  fourth,  the  branches  ti  and  o  become  separate  nerves 
(fig.  27).  From  the  posterior  portion  of  these  ganglia  a  nervous  trunk 
on  each  side  (w),  goes  to  each  foot,  where  there  is  a  small  ganglion 
(k)  sending  off  a  cutaneous  branch  and  a  branch  (^),  supplying  nerves 
to  the  foot. 

The  ganglia  (fig.  28,  e,  e)  and  the  head-ganglion  {a)  send  some  very 
slender  nerves  (fig.  28,  2,  z)  to  a  series  of  ganglia  on  the  dorsal  side  of 
the  proboscis  (y,  y).  In  figure  27  the  series  of  ganglia  {ii\  w)  are 
drawn  as  if  the  proboscis  had  been  revolved  about  a  line  drawn 
through  its  anterior  end,  so  that  the  ventral  surface  would  be  upper- 
most. In  figure  28  the  ganglia  (y,  y)  are  in  their  natural  position. 
The  dorsal  ganglia  (fig.  28,  x,  x)  are  connected  with  the  ventral 
ganglia  (fig.  27,  v,  v)  by  means  of  nervous  cords;  the  dorsal  ganglia 
(s,  s,  fig.  28)  with  the  ventral  ganglia  (fig.  27, 1, 1),  by  means  of  nerves 
[)assing  around  the  proboscis  outside  the  points  of  the  retracted  jaws 
(/,/);  and  the  dorsal  ganglia  {t,  t,  fig.  28)  with  the  ventral  ganglia 
(^5  p,  fig.27)  by  means  of  two  short,  thick  nervous  commissures  which 
send  off  the  nerves  {k,  u,  figs.  27  and  28).  These  two  nerves  {((,  u) 
terminate  in  the  ganglia  (r,  r,  figs.  27  and  28). 

These  gangba  and  iierves  of  the  proboscis  lie  on  its  walls,  under- 
neath the  muscles. 


278       F.  M.  Turnhull — Anatomy  and  Habits  of  Nereis  virens. 

The  sense-organs  are  the  four  eyes,  the  four  antennte,  the  tentacular 
cirri,  and  the  dorsal  and  ventral  cirri  of  tlie  feet ;  also  the  long  slender 
cirri  of  the  posterior  extremity.  The  antenna-  and  cirri  are  organs  of 
touch. 

Organs  of  Reproduction. 

The  sexes  are  separate,  and  the  genital  organs  appear  as  simple 
glandular  bodies,  ovaries  or  spermaries,  which  project  from  the  ven- 
tral sLiiface  into  the  cavity  of  the  body,  between  the  transverse  mus- 
cular partitions.  At  the  sexual  period  they  are  tilled  with  eggs  or 
spermatic  particles,  although  at  other  times  they  can  scarcely  be  seen. 
Neither  the  spermaries  nor  the  ovaries  have  special  excretory  ducts, 
which  open  upon  the  surface  of  the  body.  The  sperm  and  ova  are 
discharged  into  the  cavity  of  the  body,  wdiich  at  this  period  is  often 
filled  with  them.  At  the  base  of  the  lower  ramus  of  each  foot  (fig.  22, 
g)  is  a  glandular  body,  called  the  segmental  organs.  Some  of  these 
are  normally  kidneys,  as  ui-ea  has  been  found  in  them,  but  some  are 
usxxally  modified  to  act  as  oviducts,  having  a  trumpet-shaped  mouth 
opening  into  the  body  cavity  and  communicating  with  the  exterior. 
I  found  the  segmental  organs  all  along  the  body  beyond  the  region  of 
the  proboscis,  but  was  unable  to  find  the  trumpet-shaped  tubes. 
These  are  probably  situated  in  the  posterior  segments,  as  Professor 
Verrill  has  seen  the  male  worms  discharging  their  milt  from  that 
portion  of  the  body.     The  fecundation  takes  2:)lace  in  the  water. 

EXPLANATION   OF   PLATES. 
Plate  XLII. 

Figure  1. — Nereis  virens,  female;  dorsal  view  of  the  anterior  portion  of  the  body;  a, 
head,  with  four  eyes ;  6,  h,  antennte ;  c,  c,  palpi ;  c',  c',  lobes  of  palpi ;  cZ,  buccal 
ring ;  ee,  ee,  longer  dorsal  pair  of  tentacular  cirri ;  ee',  ee',  shorter  dorsal  pair  of 
tentacular  cirri ;  e,  e,  longer  ventral  pair  of  tentacular  cirri ;  e',  e',  shorter  ventral 
pair  of  tentacular  cirri;  h,  lateral  appendages;  g,  abdominal  rings. 

Fig.  2  and  2a. — Two  forms  of  setaj;  a,  shaft;  h,  blade. 

Pig_  3. — First  lateral  appendage  of  female,  posterior  view ;  lettering  the  same  as  in 
fig.  8. 

Fig.  4. — Second  lateral  appendage  of  female,  posterior  view ;  lettering  the  same  as  in 
fig.  8. 

-pig,  5. — Third  lateral  appendage  of  female,  posterior  view ;  lettering  the  same  as  in 
fig.  8. 

Pig_  6. — Fourth  lateral  appendage  of  female,  posterior  view ;  lettering  the  same  as  in 
fig.  8. 

Pig.  7. — Fifth  lateral  appendage  of  female,  posterior  view ;    lettering  the  same  as  in 


F.  M.  TnrnbuU — Anatomi/  and  Habits  of  Nereis  virens.      279 

Fig-  8. — Fortj'^-fifth  lateral  appendage  of  female,  posterior  view;  A.  upper  ramus;  B, 
lower  ramus;  a,  dorsal  cirrus;  &,  superior  ligula  of  upper  ramus;  c,  anterior 
setigerous  lobe :  /c,  posterior  setigerous  lobe ;  d,  inferior  ligula  of  upper  ramus ; 
e,  e,'  divisions  of  anterior  setigerous  lobe  of  lower  ramus  ;  /;  posterior  setigerous 
lobe;  f/,  inferior  ligula;  h,  ventral  cirrus;  i,  shoulder  of  upper  ramus;  s,  s',  sets  ; 
y,  y',  aciculEe. 

Fig.  9. — One  hundred  and  nintli  lateral  appendage  of  female,  posterior  view ;  lettering 
the  same  as  in  fig.  8. 

Fig.  10. — First  lateral  appendage  of  male,  posterior  view;  lettering  the  same  as  in 
fig.  8. 

Fig.  11.— Fifth  lateral  appendage  of  male,  posterior  view;  lettering  the  same  as  in 
fig.  8. 

Fig.  12. — Forty-fifth  lateral  appendage  of  male,  posterior  view;  '•■,  extra  division  of 
anterior  setigerous  lobe ;  x,  shoulder,  peculiar  to  the  male,  on  the  dorsal  edge  of 
the  lower  ramus ;  otherwise  the  lettering  is  the  same  as  in  fig.  8. 

Fig.  13. — One  hundred  and  ninth  lateral  appendage  of  male,  posterior  view;  lettering 
the  same  as  in  fig  8. 

Plate  XLIII. 

Fig.  15. — Nereis  virens;  ventral  view  of  the  head  and  mouth,  the  proboscis  withdrawn; 
'7,  head ;  b,  h,  antennae ;  c,  c,  palpi ;  c',  c',  lobes  of  palpi ;  d,  buccal  ring ;  ee',  ee', 
shorter  dorsal  pair  of  tentacular  cirri ;  e,  e,  longer  ventral  pair  of  tentacular  cirri ; 
e,'  e,'  shorter  ventral  pair  of  tentacular  cirri ;  ?n,  mouth  ;  g,  abdominal  rings ;  h,  h, 
lateral  appendages. 

Fig.  1  fi. — Nereis  virens;  the  walls  of  the  body  are  cut  through  longitudinally  on  the  dorsal 
side,  so  as  to  show  the  perivisceral  cavity  with  the  alimentary  canal;  m,  mouth; 
«,  muscles  of  mouth ;  x,  pharyngeal  region  of  the  proboscis ;  c,  muscular  partitions 
of  proboscis;  6,  perivisceral  cavity:  p,  dental  region  of  proboscis;  o,  oesopha- 
geal region  of  proboscis ;  j.  salivary  glands ;  r,  intestine  proper ;  a,  muscular 
partitions. 

Fig.  17.— Head  of  Nereis  virens,  with  the  proboscis  protruded,  dorsal  view;  a,  head; 
b,  b,  antennae ;  c,  c,  palpi ;  c',  c',  lobes  of  palpi ;  d,  buccal  ring ;  ee,  longer  dorsal 
pair  of  tentacular  cirri ;  ee',  ee',  shorter  dorsal  pair  of  tentacular  cirri ;  e,  e,  longer 
ventral  pair  of  tentacular  cirri ;  e',  e',  shorter  ventral  pair  of  tentacular  cirri ;  /,  /, 
jaws;  0,  anterior  median  area  of  dorsal  side;  I,  I',  left  and  right  anterior  sub- 
median  areas  of  dorsal  side ;  w,  «',  anterior  lateral  areas ;  i,  posterior  median  area 
of  dorsal  side ;  s,  s',  left  and  right  posterior  sub-median  areas  of  dorsal  side ;  ?•, 
posterior  lateral  and  ventral  areas. 

Fig.  18. — Protruded  proboscis,  ventral  side;  /, /,  jaws;  w,  w',  anterior  lateral  areas; 
y.  anterior  median  area  of  ventral  side ;  x,  %',  left  and  right  anterior  sub-median 
areas  of  ventral  side  ;  r,  posterior  lateral  and  ventral  areas. 

Fig.  19. — Jaw  of  Nereis  virens,  much  enlarged. 

Figs.  27  and  28. — Nervous  system  o(  Nereis  virens ;  h,  abdominal  ganglia;  7i,  n,  nerves 
to  muscular  partitions ;  o,  o,  nerves  passing  through  partition  to  preceding  segment ; 
TO,  m,  nervous  trunlcs  to  feet ;  k,  k,  ganglia  sending  off  a  cutaneous  branch  and  a 
branch  (i)  supplying  nerves  to  tlie  feet ;  d,  d,  connectives  ;  d',  d',  accessory  connect- 
ives ;  g,  g,  nerves  communicating  with  the  ganglia  of  the  proboscis ;  e,  e,  ganglia 
sending  branches  to  the  internal  or  ventral  tentacular  cirri ;  e',  e',  ganglia  sending 


280      F.  M.  Turiibull — Anatomy  and  Habits  of  Nereis  vlrens. 

brancbes  to  the  external  or  dorsal  tentacular  cirri ;    a,  head-ganglion  with  four 
eyes ;  h,  b,  nerves  to  antennae ;  c,  c,  nerves  to  palpi ;  iv,  iv,  series  of  ganglia  and 
nerves  on  the  ventral  side  of  proboscis ;  /,  /,  jaws,  ventral  side ;  ?/,  y,  the  series  of 
ganglia  and  nerves  on  the  dorsal  side  of  the  proboscis;  /  /  jaws,  dorsal  side. 
In  figure  27  the  proboscis  has  been  revolved  about  a  line  passing  through  g,  g,  so 
that  the  ventral  side  is  uppermost.     The  head  and  abdominal  ganglia  are  in  their  nat- 
ural position.     The  position  of  figure  28  is  reversed  so  as  to  show  the  relations  of  the 
dorsal  ganglia  y,  y,  to  the  ventral  ganglia  w,  w  (fig.  27). 

Plate  XLIV. 

Fig.  20. — Circidation  of  blood  in  Nereis  virens,  and  also  the  alimentary  canal  in  its 
natural  position ;  to,  mouth ;  x,  pharyngeal  region  of  proboscis ;  p,  dental  region 
of  proboscis;  o,  oesophageal  region  of  proboscis;  r,  intestine,  covered  with  a 
vascular  network,  which  is  connected  in  each  segment  with  the  large  dorsal  and 
ventral  vessels  by  short  Ijranches ;  j,  salivary  glands ;  a,  large  dorsal  vessel ;  b. 
large  ventral  vessel;  c,  c',  c'',  peripheral  vessels;  d,  branches  from  the  dor- 
sal side  of  the  feet;  e,  branch  to  oesophagus  ;  /,  /'',  branches  to  the  ventral  side 
of  the  feet;  s,  lateral  branch,  supplying  the  vascular  network  {g)  and  first  three 
lateral  appendages;  A",  vessel  from  network  (g)  to  base  of  tentacular  cirri;  t, 
branch  from  the  vascular  network  (u)  on  the  proboscis,  to  the  large  ventral  vessel 
(6) ;  V,  branch  from  the  large  dorsal  vessel  (a),  at  base  of  head,  to  the  network  (u) 
on  the  proboscis. 

Fig.  21. — Diagram,  showing  the  disposition  of  the  large  ventral  vessel,  and  its  branches 
on  both  sides,  in  the  anterior  portion  of  the  body ;  I,  continuation  of  the  large 
ventral  vessel  along  the  median  ventral  line  beneath  the  muscles  of  the  proboscis ; 
n,  vascular  ring  surrounding  tlie  pliaryngeal  region  of  proboscis ;  otherwise  the 
lettering  is  the  same  as  in  fig.  20.  The  arrows  indicate  the  direction  in  which 
the  blood  flows. 

Pig.  22. — Diagram  to  show  the  circulation  of  the  blood,  and  also  the  relative  position 
of  the  parts,  in  one  segment  of  the  body ;  i,  intestine  ;  p,  perivisceral  cavit_y ;  h, 
crypt  from  which  aciculee  grow ;  1.  muscles  of  crypt,  which  are  attached  to  the 
base  of  the  foot ;  g,  g,  segmental  organs ;  k,  walls  of  body ;  n,  a  ganglion  of  the 
abdominal  chain;  «,  large  dorsal  vessel;  b,  large  ventral  vessel;  c,  peripheral 
vessel ;  /,  branch  to  ventral  side  of  foot ;  d,  branch  from  dorsal  side  of  foot. 

Fig.  23. — Circulation  of  the  blood  in  the  last  posterior  segment ;  a,  large  dorsal  ves- 
sel ;  6,  large  ventral  vessel ;  c,  vascular  ring,  with  no  branches. 

Fig.  24. — Lateral  view  of  the  circulation  in  one  segment;    d,  branch  from  the  dorsal 
side  of  foot:  /,  branch  to  the  ventral  side  of  foot  in  the  adjacent  posterior 
segment. 
In  the  last  two  figures  arrows  indicate  the  direction  in  which  the  blood  flows. 

Fig.  25. — Dorsal  view  of  two  segments  showing  the  vascular  network  in  the  lateral 
appendages  and  beneath  the  skin  of  the  back;  lettering  the  same  as  in  fig.  22  ; 
the  large  dorsal  vessel,  a,  and  the  peripheral  vessels  c,  c,  show  through  the  trans- 
lucent walls  of  the  body. 

Fig.  26. — Segment  showing  the  vascular  network  beneath  the  skin  of  the  ventral  side 
and  in  the  lateral  appendages;  lettering  as  in  fig.  22. 


VII.    Median  and  Paired    Fins,  a  Contribution   to   the    His- 
tory OF  Vertebrate  Limbs.     By  James  K.  Thacher. 

Median  Fins  in  Amphioxus. 

The  quadrate  markings  seen  at  the  base  of  the  median  fin  in 
Amphioxus  extend  on  the  dorsal  side  from  one  extremity  of  the 
animal  to  the  other,  or  nearly  so,  and  on  the  ventral  side  from  the 
porus  abdominalis  aboi-ad  toward  the  extremity  of  the  tail.  They 
are  largest  and  most  distinct  in  the  middle  of  the  body,  and  become 
smaller  and  less  clearly  marked  (as  seen  from  the  outside),  toward 
the  head  and  tail  until  they  seem  to  fade  out  entirely  as  they  closely 
approach  these  extremities. 

As  Stieda*  has  shown  these  are  but  the  external  marks  of  a  series  of 
cavities,  containing  what  is  described  as  "  a  transparent,  wholly  struc- 
tureless mass,  resembling  a  coagulation." 

Thus  the  relation  of  these  bodies  to  the  somewhat  similarly  placed 
primordial  tin  rays,  or  "interneural  spines,"  of  the  Craniote  fishes  is 
not  so  simple  and  direct  as  indicated  in  the  mistaken  repi-esentations 
of  Rathkef  and  of  Mtiller.J  Still  they  occupy  a  position  similar  to 
that  of  the  primordial  fin  rays  of  other  fishes,  and  the  fact  that  they  di» 
not  agree  with  the  segmentation  of  the  lateral  muscles,  seems  to  have 
some  pertinency  here,  and  to  this  alone  I  wish  to  call  attention. 

In  the  middle  of  the  back  there  are  about  five  of  these  bodies  to  a 
single  segment,  and  on  the  ventral  side  just  aborad  of  the  abdominal 
pore  there  are  about  four  to  each.  As  we  shall  see  hereafter,  the 
structures  of  the  median  line  (genuine  fin-rays  except  in  Amphioxus) 
exhibit  quite  generally  throughout  the  fishes,  a  total  disregard  of 
the  segmentation  of  the  lateral  muscles,  and  are  more  numerous  than 
those  segments. 

*  Studien  iiber  den  Amphioxus  lanceolatus  von  Dr.  Ludwig  Stieda,  Mem.  de  I'Acad. 
Imp.  des  Sciences  de  St.  Petersbourg,  VII^  Serie,  Tome  xix,  No.  7. 

f  Rathke,  Bemerkungen  liber  den  Ban  des  Amphioxus  lanceolatus.  Konigsberg, 
1841. 

X  Johannes  Miiller,  Ueber  den  Bau  and  die  Lebensersclieinungen  des  Branch iosioma 
lubricum.  Abhandl.  der  Berliner  Academic,  1842. 

Trans.  Conn.  Acad.,  Vol.  III.  36  February,  1877. 


282  ./.  K.  Tharher — MedUm  and  Paired  Fins. 

Median  Fins  in  Myxina. 

In  Myxine  'glutinosa  the  median  tin  extends  but  a  short  distance 
forward.  In  a  specimen  24  centimeters  long,  from  the  Bay  of  Fundy, 
the  fin  reaches  4  cm.  from  the  extremity  of  the  tail  on  the  dorsal  side, 
and  2*5  on  the  ventral. 

The  fin-rays,  now  unquestionable  homolognes  of  the  ])rimordial  fin- 
rays  of  Gnathostomes,  tliough  not  yet  having  assumed  the  histologi- 
cal structure  of  true  cartilage,  support  the  thin  fold  of  skin  which 
forms  the  fin.  They  are  simple  tapering  rods,  extending  distally  to 
the  edge  of  the  fin,  and  proximally  scarcely  dipping  below  the  general 
body  contours. 

The  only  deviation  from  sim])le  rods  which  I  have  been  able  to  find 
is  the  dichotomous  splitting  of  some  of  the  rods  where  the  fin  rounds 
the  extremity  of  the  tail. 

The  numerical  relation  between  these  rays  and  the  corres})onding 
muscular  segments  is  as  three  to  one  on  the  dorsal  side,  and  as  two 
and  a  half  to  one  on  the  ventral. 

I  have  been  iinable  to  detect  any  muscular  fibers  in  the  composi- 
tion of  the  fin. 

Median  Fins  in  Petromyzon. 

Here  the  median  fins  are  much  better  developed.  In  a  specimen 
(^Petromyzon  marinus,  from  the  Connecticut  River),  77  cm.  long,  the 
caudal  fin  extends  forward  along  tlie  dorsal  side  7*5  cm.,  sloping 
downward  nearly  to  the  body,  then  tlie  second  dorsal  rises  abruptly  and 
runs  orad  16  cm.,  where  it  reaches  by  a  gentle  slope  the  general  out- 
line of  the  body.  There  follows  a  finless  space  ;1"5  cm.  in  length 
which  is  succeeded  by  the  first  dorsal,  whose  extent  is  9  cm.,  being 
therefore  shorter  as  it  is  lower  than  the  second  dorsal.  The  anus  is 
opposite  the  orad  part  of  the  second  dorsal. 

The  fins,  therefore,  take  up  almost  the  whole  of  the  hinder  half  of 
the  mid-dorsal  line.  In  Myxine  only  one-sixth  was  thus  occupied. 
On  the  ventral  side  we  have  only  the  caudal,  extending  about  as  far 
here  as  it  does  above. 

These  fins  are  sup})orted  by  a  series  of  chondroid  rays,  lying  quite 
close  to  one  another  in  the  median  plane.  They  are  straight  and  slope 
aborad  from  the  fatty-fibrous  ridge-pole  of  the  myelonal  canal  (PI. 
XLIX,  fig.  1,  a,)  to  the  very  edge  of  the  fin.  They  are  found  in  all  the 
fins.  Their  form  is  represented  in  PI.  XLIX,  fig.  1,  where  only  one 
ray  is  drawn  complete.  As  shown,  it  bifurcates  twice  and  thus  ends 
distally  in  four  fine  branches.      This  figure  is  IVom  the  central    p.'irt  of 


J.  K.  Thdcher — Mediati  and  Paired  Fins.  283 

tlu'  lartio  second  dors.al,  and  sliows  one  of  the  longest  rays.  Where 
they  are  shorter  we  may  liave  only  one  bifurcation,  or  one  of  the  two 
l)riniary  branches,  that  toward  the  longer  rays,  may  again  divide, 
while  the  other  toward  the  shorter  remains  uncleft.  Farther  forward 
at  the  beginning  of  the  second  dorsal,  where  the  rays  are  still  shorter, 
they  do  not  divide  at  all,  but  end  somewhat  bluntly  though  com- 
pressed from  side  to  side. 

Each  ray  is  largest  in  the  middle  and  here  lies  quite  close  to  its 
adjacent  rays  ;  below  they  grow  more  slender,  and  therefore  are  some- 
what spaced,  but  expand  somewhat  to  a  foot  resting  on  the  myelonal 
canal. 

I  have  seen  no  cases  of  concrescence  between  adjacent  rays.  With 
the  exception  of  the  variation  in  the  branching  and  length  in  different 
parts  of  the  fin,  before  alluded  to,  the  rays  are  all  similar  and  parallel 
one  to  another. 

This  branching  is  plainly  a  true  dichotomy  and  not  the  product  of 
concrescence,  as  is  evidenced  by  the  total  absence  of  anything  else 
resembling  concrescence,  by  the  similarity  in  size  between  two  adja- 
cent differently  branched  rays,  and  by  the  regularity  of  the  branching. 

On  each  side  of  the  row  of  skeletal  elements  are  muscular  bundles 
of  a  somewhat  blacker  color  than  the  two  great  masses  of  lateral 
muscles.  The  muscles  of  the  median  fin  wedge  themselves  into  the 
angle  between  the  lateral  muscles  of  the  two  sides  along  the 
median  line.  They  ai-e  sharjdy  distinguished  from  these.  The  fibers 
of  the  lateral  muscles  run  longitudinally,  while  those  of  the  fin  mus- 
cles are  parallel  to  the  pi'iniordial  median  fin-rays.  There  is  abso- 
lutely no  continuity  between  the  two  in  any  part.  Moreover  the 
bundles  of  the  fin-muscles  show  no  relations  to  the  segments  of  the 
lateral  muscles.  A  cross  section,  PI.  XLIX,  fig.  3,  shows  the  relation 
between  the  fin-muscle  bundles  and  fin-rays. 

The  numerical  relation  between  the  fin-rays  and  the  segments  of 
the  lateral  muscle  is  shown  in  PI.  XLIX,  fig.  2,  where  we  have  a  little 
less  than  four  of  the  former  to  one  of  the  latter. 

The  relation  between  the  tin-rays  and  the  neural  arches  is  shown 
in  figure  1,  where  we  have  35  rods  and  23  arches.  These  neural 
arches  rise  from  the  sheath  of  the  notochord,  to  stiffen  the  fibrous 
sides  of  the  myelonal  canal  and  to  apply  themselves  to  its  fatty- 
fibrous  ridge-pole.  The  fin-iays  abut  on  the  same  ridge-pole  in  the 
mid-dorsal  line,  but  they  are  in  no  way  connected  with  the  neural 
arches.  1  have  met  with  no  cases  even  of  concrescence  between  the 
two. 


284 


./  K.  Thacher — Median  and  Faired  Fins. 


Figure  4,  PI.  XLIX,  shows  the  relation  between  the  neural  arches 
and  the  segments  of  the  lateral  muscles.  There  are  two  arches  to 
one  seo-ment.  In  fio-ure  1,  then,  there  must  have  been  lU  segments, 
which  gives  us  a  very  little  more  than  three  as  the  ratio  between  the 
fin-rays  and  the  segments.  From  figure  2  we  obtained  a  little  under 
four.  Both  results  are  necessarily  correct.  There  is  considerable 
variation  in  the  relation  between  the  fin-rays  and  the  muscular  seg- 
ments and  the  neural  arches.  This  is  exhibited  in  the  following  table 
of  observations  on  a  single  specimen. 


Fin-raj's. 
19 

Arches. 

Katio  of 

fln-rays  to 

arches. 

Ratio  of 
fln-rays  to 
segments. 

In  the  orad  half  of  ID. 

8 

2-4 

4-8 

In  the  aborad  half  of  ID. 

20 

8 

2-5 

5- 

In  the  orad  part  of  2D. 

20 

11 

1-8 

3-6 

In  the  next  35  rays  of  2D. 

35 

23 

1-5 

3- 

In  the  next  1*1  rays  of  2D. 

27 

17 

1-6 

3-2 

In  the  next  12  rays  of  2D. 

12 

7 

1-7 

3-4 

The  Lampreys  then  have  advanced  beyond  the  Myxines  toward 
the  Gnathostomes  as  regards  the  structure  of  the  median  fins,  in  the 
greater  development  and  efficiency  of  those  organs,  and  in  the  addi- 
tion of  special  fin-muscles  whioh  seem  to  be  wanting  in  the  lower 
group.  And  while  in  Myxine  the  original  independence  of  the 
median  fin  skeleton  and  the  axial  skeleton  is  shown  by  the  e.vistence 
of  the  median  fin-rays  before  any  neural  arches  have  appeared,  and 
by  their  want  of  agreement  with  the  musi-ular  segments  to  which  the 
axial  skeleton  will  conform  when  it  does  arise,  in  Petromyzon  we 
have  the  same  independence  more  strikingly  reaflirmed  by  the  simul- 
taneous existence  of  neural  arches  and  median  fin-rays,  and  their 
perfect  indifference  to  one  another. 

Median  Fins  of  Elasinobranchii.* 
We  shall  here  consider  the  skeleton  of  the  dorsal  and  anal  fins  alone. 
That  of  the  caudal  fin  has  on  the  ventral  side  undergone  peculiar 
modifications  by  the  union  of  tin-rays  with  hnemal  s[)ines. 

*  The  term  Elasmobranchii  includes  the  Chimaeroids  with  the  Sharks  and  Rays.  I 
have  had  no  opportunity  of  examining  the  tin  skeletons  of  the  former.  But  Chimaera 
seems  to  me  to  be  but  a  divergent  form  of  Sharks  and  to  have  its  nearest  living 
relative  in  Cestracion.     They  are  quite  specialized  forms,  Cestracion  the  less  so. 

I  will  state  here  that  the  Elasmobranchs  described  came  from  Wood's  Hole,  Mass. 
The  names  used  are  those  given  by  Dr.  Gill  in  the  IT.  S.  Fish  Coram.  Rep.  for 
1871-72. 


J.  K.  Tharhr)' — Median  and  Paired  Fins.  '285 

In  general  the  ^<l^u•tul•e  of  tlie  medi.-ui  tin  resembles  wliat  we  have 
seen  in  Petromyzon,  but  there  are  important  differences.  The  rays 
are  of  hyaline  cartilage  and  they  do  not  usually  reach  down  to  the 
ridge-pole  of  the  myelonal  canal.  In  EKlamla,  for  example,  in  tlie 
smaller  of  the  specimens  %ured,  the  rays  approach  within  a  centime- 
ter and  a  half  at  the  oiad  extremity  of  the  first  dorsal  fin,  but  are 
three  and  a  half  centimeters  distant  at  the  other  extremity.  In 
Si/ualus  {Ae(()ifh)as)  they  come  closer. 

This  ridge-pole  consists  of  a  cord  of  rather  peculiar  white  lono-i- 
tudinal  fibers,  constituting  now  a  ''  liyauieatuin  longltitdinale.''''  It 
appears  to  me  undoubtedly  homologous  with  the  fatty-fibrous  body 
in  Petromyzon.  The  cartilaginous  arches  unite  under,  and  do  not 
extend  around  over  it,  though  they  clasp  it  somewhat. 

The  rays  are  segmented,  usually  twice.  Dichotomy  is  rare  if  not 
altogether  absent.  Concrescence  of  adjacent  rays  is  by  no  means 
uncommon.     The  reduction  of  rays  in  size  is  exhibited  in  all  deo-rees. 

Calcification  presents  itself  in  a  thin  superficial  layer  on  each  side 
of  the  somewhat  flattened  ray,  but  it  fails  on  the  edges,  i.  e.  as  we 
come  close  to  the  median  plane. 

The  muscles  of  the  fin,  as  in  Petromyzon,  are  in  total  independ- 
ence of  the  large  masses  of  segmented  lateral  muscles,  but  they  are 
in  more  definite  relation  with  the  skeleton  of  the  fin.  This  is  accu- 
rately represented  in  PI.  LIX,  fig.  66,  though  that  is  a  s-;ction  of  a 
pectoral  and  not  of  a  median  fin.  We  see  that  each  ray  has  on  each 
side  a  special  muscle,  separated  from  its  fellows  by  the  fibrous  sheet 
which  runs  from  between  the  rays  to  the  integument.  Each  little 
muscle  developes  in  its  median  line  a  flat  tendon,  which,  parallel  to 
the  surface  of  the  fin,  inserts  itself  in  the  fascia  covering  the  extremi- 
ties of  the  fin-rays  and  the  proximal  ends  of  the  well  known  horny 
fibers,  which  here  supplement  the  primordial  skeleton,  as  the  second- 
ary fin-rays  of  Ganoids  and  Teleosts  do. 

The  relation  between  the  niimber  of  fin-rays  and  that  of  the 
vertebra?  opposite  to  them  is  similar  to  what  we  ha^e  seen  in  the 
lower  forms.  In  the  Nictitantes,  for  example,  there  are  on  the  average 
about  '2-5  rays  to  one  vertebra.  But  there  is  considerable  variation, 
even  in  individuals  of  the  same  species.  The  extreme  numbers,  so  far 
as  I  have  observed,  are  3 '5  in  an  anal  of  Sphyrna,  and  2  in  a  first 
dorsal  of  Eulamia. 

We  turn  now  to  the  more  minute  examination  of  several  species.. 


286  ./.  K.  ThacJier — Median  and  Paired  Fins. 

First  Dorsal  of  Mustelus  cants,  PI.  XLIX  and  L,  figs.  5-10. 

Id  pi.  XLIX,  fig.  5,  we  have  24  separate  rods,  unless  ?>  be  the  terminal  piece  of  2  ; 
but  its  conformation  seems  to  testif}'  to  its  independent  but  reduced  character.  The 
number  here  then  is  24  or  2,3. 

In  PI.  XLIX,  fig.  6.  we  have  again  the  same  alternative,  witliout  quite  so  strong  a 
case  for  24,  but  still  quite  strong. 

In  PI.  L,  fig.  7,  we  have  the  choice  between  24  and  2.5,  but  in  favor  of  the  latter. 

In  PI.  L,  fig.  8,  we  have  23  or  24,  but  the  former  has  the  greater  probability. 

PI.  L,  fig.  9  gives  us  22,  23  or  24,  23  being  more  probable. 

PL  L,  fig.  10  exhibits  23  or  24,  dependent  on  the  view  taken  of  rays  5,  6,  and  7. 
The  probability  seems  in  favor  of  24. 

I  think  we  may  sum  up  then  with  regard  to  the  number  of  rays  constituting  the 
first  dorsal  of  Mitslelus  canis  thus :  it  has  usually  24  rays  but  this  may  vary  to  23  or  25. 

Nearly  all  the  rods  are  segmented  twice.  The  distal  line  of  segmentations  fails  in 
the  one  or  two  orad;  and  the  proximal,  in  the  two  or  three  aborad  ones.  Additional 
segmentations  are  ver}'  rare.  What  might  be  reckoned  as  such  are  seen  in  fig.  7,  ray 
4 ;  fig.  6,  rays  5  and  6.     This  makes  an  average  of  ■()  +  .* 

The  union  of  adjacent  rays  is  rare.  I  estimate  it  at  '04  of  the  total  possible  con- 
crescence.f 

Shortening  or  reduction  in  size  is  likewise  rare.  We  have  first  those  questionable 
cases  of  which  fig.  5,  rod  3  seems  the  least  questionable ;  and  then  plainer  but  less 
extreme  instances  in  fig.  7,  ray  5;  fig.  9,  ray  18;  fig.  10.  ray  7,  then  we  have  the  usual 
shortening  of  the  rays  at  the  extremities  of  the  fin.  When  these  aborad  rays  shorten 
up,  those  next  in  front  of  them  have  a  remarkable  tendency  to  grow  up  under  them. 
This  is  well  shown  in  fig.  9. 

iforeover  when  in  the  aborad  rays  the  proximal  joint  becomes  very  short,  it  is  some- 
times divided  into  two  lateral  halves.     This  is  the  case  for  example  in  rod  22  of  fig.  10. 

Occasionally  we  have  a  minute  piece  or  pieces  of  cartilage  forming  a  tip  to  a  ray. 
It  cannot  act  as  an  extra  joint,  by  giving  increased  flexibility  to  the  ray.  And  it 
seems  doubtful  whether  the  origin  of  the  two  is  to  be  referred  to  the  same  causes. 
Yet  intermediate  forms  occur  so  as  to  raise  the  question  whether  they  are  to  be 
referred  to  one  or  the  other  category.    Tliese  tips  seem  to  ))e  exhibited  in  fig.  7,  ray  4 ; 

fig.  8,  rays  2  and  3 ;  fig.  9,  ray  3.     This  gives  „ — -  —  0  +  . 

I  now  find  the  ratio  of  the  proximal  piece  of  the  middle  ray  of  each  tin  to  the 
middle  piece  of  the  same.  The  average  of  these  ratios  is  -6.  The  method  gives  -3  as 
the  ratio  between  the  terminal  and  middle  joints. 

We  have  then  for  the  first  dorsal  of  Mustelus  canis : 

Number  of  rays  24.     Extra  segmentations  '0  + . 

Concrescence '04.  Betipping -0  +  .  Katio  of  proximal  to  middle  piece  of  middle 
ray  -6.     Ratio  of  distal  to  middle  piece  -3. 


*  The  decimal  is  obtained  by  dividing  the  number  of  additional  segments  by  the 
number  of  rays. 

\  The  amount  of  concrescence  between  two  adjacent  rays  is  the  ratio  between  the 
length  of  the  union  and  the  whole  distance  through  which  they  are  adjacent  and 
might  have  united.  The  sum  of  these  fractions  divided  by  the  number  of  rays  less 
the  number  of  fins,  gives  the  estimate  of  the  concrescence. 


J.  K.  TharJier — Median  and  Paired  Fins.  287 

Second  Dorsal  of  Mvstelus  cams,  PI.  L  and  LI,  figs,  ll-lf). 

Fig.  11  has  24  rays.  fig.  12  has  22.  fig.  13  has  2:i,  fig.  14  has  24,  fig.  15  has  24.  Tluis  of 
the  five  examined  three  have  24,  one  23  and  one  22  rays.  It  seems  probable  that  a 
wider  examination  would  give  as  forms  having  25  or  more  rarely  2().  Thus  we  have 
for  the  second  dorsal  24  rays  with  some  slight  variation. 

Extra  segmentations  appear  only  in  fig.  11,  ray  5 ;  and  fig.  14,  ray  2.    Tliis  gives  -0  + . 

I  estimate  the  concrescence  at  -06.  The  concrescence  is  mostly  confined  to  tlie 
proximal  row,  and  is  more  frequent  at  the  two  ends  than  in  the  middle  of  the  series. 

Betipping  is  seen  only  in  fig.  14,  ray  23.     This  gives  ^0  + . 

Ratio  of  proximal  piece  of  middle  ray  to  middle  piece  '6. 

Ratio  of  distal  piece  of  middle  ray  to  middle  piece  -4. 

Tlie  downward  prolongation  of  the  proximal  parts  of  one  or  two  of  the  orad  ra^-s  is 
noticeable,  being  quite  pronounced  in  all  the  cases  except  that  represented  in  fig.  1 1 . 

The  reduction  of  the  rays  is  rare,  but  shown  to  an  extreme  extent  in  fig.  11,  ray  1  ; 
and  fig.  15,  ray  1. 

Anal  of  Mustelus  canis,  PI.  LI  and  LII,  figs.  16-19. 

Figs.  16  and  17  have  each  18  rays.  Fig.  18  has  IT  or  18  according  as  the  last  ray 
is  double  or  not.  Fig.  19  has  18  or  19  under  the  same  conditions.  The  great  width 
of  the  last  ray  in  the  last  two  cases  makes  the  larger  number  probable.  Thus  we 
have  18  as  the  normal  number,  with  probably  slight  variations. 

Extra  segmentations  are  seen  in  fig.  17,  ray  5  ;   and  fig.  19,  ray  3.     This  gives  '0  +  . 

The  concrescence  I  estimate  at  -09.  Betipping  occurs  in  fig.  16,  ray  3.  This  gives  "0  + . 

Ratio  of  proximal  piece  of  middle  ray  to  middle  piece  is  -I. 

Ratio  of  distal  piece  of  middle  ray  to  middle  piece  is  "6. 

First  Dorsal  of  Galeocerdo  tigrinus,  PI.  LII,  fig.  20. 

In  this  sole  specimen  there  are  25  rays. 

Extra  segmentation  occurs  in  10,  20,  21.  22,  23,  which  gives  -2.  It  should  be 
noticed  that  this  extra  segmentation  is  in  each  case  here  a  doubling  of  the  proximal 
line  of  segmentations. 

Concrescence  is  estimated  at  -06.    Betipping  is  seen  in  18,  19  and  25.   This  gives  '1. 

Ratio  of  proximal  piece  of  middle  ray  to  middle  piece  1-1. 

Ratio  of  distal  piece  of  middle  ray  to  middle  piece  -6. 

Shortening  is  seen  in  6  and  22.  In  the  latter  the  proximal  piece  is  ext  luded  from 
the  edge  of  the  fin  by  a,  the  proximal  piece  of  2;!,  and  by  the  proximal  piece  of  21. 
The  piece  a  consists  of  two  lateral  halves. 

Second  Dorsal  of  Galeocerdo  tigrinus,  PL  LII,  fig.  21. 
Number  of  rays  13.     Extra  .segmentation  in  3,  giving  -1. 
Concrescence  is  estimated  at  -01.     Betipping,  in  5,  8  and  13,  gives  -2. 
Ratio  of  proximal  piece  of  middle  ray  to  middle  piece  1-3. 
Ratio  of  distal  piece  of  middle  ray  to  middle  piece  -6. 

Anal  of  Galeocerdo  tigrinVjS,  PI.  LII,  fig.  22. 
Number  of  rays  12.     Extra  segmentation  in  6,  7.  8  and  10.  gives  3. 
Concrescence  is  estimated  at  -05.     Betipping  in  4  gives  "l. 
Ratio  of  proximal  piece  of  middle  ray  to  middle  piece  I'l. 
Ratio  of  distal  piece  of  middle  ray  to  middle  piece  -7. 


288  ./  K.  Thacher — Median  a7id  Paired  Fins. 

First  Dorsal  of  Eulamia  Milherti,  PI.  LII  and  LIU,  figs.  28  and  24. 

Number  of  rays  28  or  29.  ^ 

As  indicated  by  the  numbering  of  the  rays,  I  take  number  21  in  each  figure  to  be  a 
single  ray,  which  has  widened  at  the  top,  and  been  segmented  in  the  way  figured. 

Extra  segmentations  in  fig.  23.  rays  20  and  21  (2  extra  segmentations  in  the  latter) 
in  fig.  24,  rays  4  and  21.     This  gives  •!. 

Concrescence  is  estimated  at  -09.     Betipping  is  absent. 

Ratio  of  proximal  to  middle  piece  •9. 

Ratio  of  distal  to  middle  piece  '9. 

Second  Dorsal  of  Ealamia  Milherti,  PI.  LIU.  figs.  25  and  26. 

The  number  of  rays  differs  remarkably  in  the  two  specimens,  being  12  in  the  one 
and  16  in  the  other.  It  must,  however,  be  remembered  that  the  second  dorsal  has 
become  very  small  and  of  very  little  physiological  importance.  Organs  which  have 
thus  become  functionless  are  peculiarly  prone  to  vary.  They  thus  secure  more  easily 
some  other  and  new  function.  We  will  take  the  average  number  14  as  the  normal  one 
for  the  rays  of  this  fin. 

Extra  segmentation  occurs  in  fig.  25,  ray  6  (twice),  and  in  fig.  26,  ray  3  This 
gives  •!. 

Concrescence  is  estimated  at  -09. 

Betipping  is  absent. 

Ratio  of  proximal  to  middle  piece  of  middle  ray  -8. 

Ratio  of  distal  to  middle  piece  of  middle  ray  -5. 

Anal  of  Etdamia  Milherti,  PL  LIII,  figs.  27  and  28. 

Number  of  rays  17  or  18. 

Extra  segmentations  in  fig.  27,  rays  7,  10  and  12  (twice  in  the  latter);  in  fig.  28, 
twice  in  12,  once  in  16,  give  2. 

This  implies  a  certain  interpretation  of  the  ambiguous  rays  11  and  12  in  figure  27. 
In  fig.  28  we  seem  to  have  a  plain  case.  Here  the  ray  1 2  is  broadened  at  the  top,  and 
its  distal  piece  divided  by  two  intersecting  cuts  into  four  pieces.  Ray  12  in  fig.  27  is 
explained  in  the  same  way.  Ray  11  is  a  little  shortened,  and  excluded  from  the  edge 
by  the  tips  of  10  and  of  12.     This  appears  to  me  the  most  probable  view  of  the  case. 

Concrescence  is  estimated  at  ■12.     Betipping  absent. 

Ratio  of  proximal  to  middle  piece  of  middle  ray  -7. 

Ratio  of  distal  to  middle  piece  of  middle  ray  -4. 

First  Dorsal  of  Sphyrna  zygcena,  PI.  LIII  and  LIV.  figs.  29  and  30. 

Number  of  rays  33  and  34. 

I  regard  the  three  pieces  at  the  extremity  of  28  as  belonging  to  that  ray.  It  has 
been  widened  and  divided  like  the  instances  in  Eula.mia. 

Extra  segmentations,  fig.  29,  rays  2  and  3,  twice;  rays  4  and  5;  ray  28,  twice;  fig. 
30,  ray  28,  twice,  give  -2. 

Concrescence  is  estimated  at  -07.     Betipping  absent. 

Ratio  of  proximal  piece  of  middle  ray  to  middle  piece   7. 

Ratio  of  distal  to  middle  piece  of  middle  ray  2-4. 

In  fig.  29  the  proximal  line  of  segmentation  fails  in  rays  9-17,  except  in  the  joined 
rays  U  and  12  where  it  is  present.     In  fig.  30  it  fails  in  rays  8-16. 


J.  K.  Thacher — Median  and  Paired  Fins.  289 

Second  Dorsal  of  Sphyrna  zygcena,  PL  LIV,  tig.  31. 
Number  of  rays  14.     Extra  segmentations  amount  to  10. 
Concrescence  is  estimated  at  '07. 
Betipping  is  absent. 

Ratio*  of  proximal  to  middle  piece  of  middle  ray  -3. 
Ratio  of  distal  to  middle  piece  of  middle  ray  -3. 
The  last  ray,  both  in  the  second  dorsal  and  the  anal,  is  large  and  round. 

Anal  of  Sphynia  zygana,  PI.  LIV,  fig.  32. 
Number  of  rays,  27. 

Extra  segmentations  8  (1),  9  (1),  10  (1),  11  (1),  12  (1),  13  (1),  14  (1),  15  (1),  16  (1), 
17  (i),  18  (2),  19  (1),  20  (1).     This  gives  "5. 

Concrescence  is  estimated  at  -03.  Betipping  none. 
Ratio  of  proximal  to  middle  piece  of  middle  ray  -4. 
Ratio  of  distal  to  middle  piece  of  middle  ray  -3. 

First  Dorsal  of  Eugoynpliodus  litoralis,  PI.  LIV,  and  LV,  tigs.  33-39. 

Specimens  figured  in  tigs.  33,  34  and  36  have  plainly  16  rays.  Those  in  figs.  37 
and  39  have  plainly  17.  Those  in  tigs.  35  and  38  have  16  separate  rays,  but  the  last 
is  quite  broad.  Where  we  have  plainly  17  rays,  figs.  37  and  39,  the  last  two  rays 
have  united  with  the  exception  of  their  distal  joints.  We  may  fairly  conclude  that 
figs.  35  and  36  present  a  more  complete  concrescence  of  those  rays.  We  have  then 
as  the  number  of  rays  16  or  17,  the  former  in  three  cases,  the  latter  in  four. 

Extra  segmentation  is  estimated  at  '7.     Concrescence  is  estimated  to  be  "05. 

Betipping  reaches  -4,  each  separate  piece  being  counted.  These  small  nodules  of 
cartilage  sometimes  seem  very  evidently  to  be  a  continuation  of  a  ray  upon  the  fol- 
lowing ray.  But  not  infrequently  they  seem  to  be  scattered  rather  irregularly  along 
the  edge  of  the  fin.  It  will  be  noticed  that  they  are  most  frequent  in  the  orad  part 
of  the  fin,  though  not  on  the  first  two  or  tliree  rays.  It  is  very  probable  that  the 
estimate  of  their  frequency  should  be  higher  than  given,  for  they  are  easily  lost  in 
the  preparation  of  the  specimen. 

Ratio  of  proximal  to  middle  piece  of  middle  ray  -5.  Ratio  of  distal  to  middle  piece 
of  middle  ray  -4. 

Second  Dorsal  of  Eugomphodus  lltoralis,  PI.  LV  and  LVI,  figs.  40-46. 

In  fig  42  we  have  16;  in  45,  17  ;  in  40  and  46  we  have  18  rays.  These  are  all  plain 
cases.  Fig.  43  exhibits  17  rays,  but  raises  a  suspicion  of  18  by  the  breadth  of  the 
last  ray.  Pig.  41  gives  16  or  17,  probably  the  latter.  Fig.  44  leaves  us  in  doubt 
between  14,  15  and  16,  with,  as  it  seems  to  me  15,  the  most  probable.  We  may  take 
17  as  the  normal  number.  As  far  as  the  evidence  here  goes  the  second  dorsal  is 
more  liable  to  vary  than  the  first.  We  see  that  in  each  the  greater  the  number  of  rays, 
the  greater  is  the  amount  of  concrescence. 

Extra  segmentation  amounts  to  "6. 

Concrescence  amounts  to  -10.     Betipping  amounts  to  -4. 

Ratio  of  proximal  to  middle  piece  of  middle  ray  is  '3. 

Ratio  of  distal  to  middle  piece  of  middle  ray  is  -3. 

*  Where  a  segmentation  is  double  the  point  half  way  between  the  joints  is  taken  as 
the  limit  between  the  middle  and  extreme  piece.  Where  it  is  triple  the  middle  seg- 
mentation is  taken. 

Trans.  Coxn.  Acad.,  Vol.  III.  37  February,  1877. 


290 


./.  K.   T/iiichn' — Median  a  ml  I'dircd  hlnx. 


Amil  of  Eugompliodua  Ulorulis,  1*1.  L\'l  and  LVIl,  (i<;'s.   17-5(1. 

The  number  of  rays  is  21  in  figs.  47  iiiul  -49.  In  18  \\v  liavo  'I'l,  and  in  50,  'JO  rays. 
We  may  take  then  21  as  the  normal  nunilicr. 

Extra  sogmoiitations  amount  to    1. 

ConcTOSoonco  is  estimated  at  ■]().     Hetippin^-  amounts  to  •:{. 

Ratio  of  proximal  to  middle  piooo  of  middle  ray  i. 

Ratio  of  distal  to  middle  pieee  of  middle  ray   5. 

Wo  may  sum  up  the  results  of  this  investigation  of  the  reseiul)lani'es  and  dillercnces 
of  the  forms  so  far  examined  in  the  following  table. 


No.  of  Kxtra  ( ion- 

rays.    seKliU'iitatioiiH.  (■iH'HC'ciicc.  Brli|i|iiii; 


Katio  of       Hatlo  ot 
|.ro\.  to    (Uwtal  to  iiild. 

mid.  i>ic('(^   pk'co  of  mill. 

)riiii(l.rHV.        rav. 


First 
Dorsal. 


Second 
Dorsal. 


Anal. 


i'lugomphodus  . .  17 

Mnstelus 21 

(lalooeerdo 25 

K\damia 29 

Spliyrna :M 

i^yugomphodua  _ .  17 

Mnstelus    21 

(lalooeerdo 1  :i 

Eulaiuia II 

Sphyrna -II 

'  Mugomphodus  ..21 

Muslelus 18 

Oaleoeordo 12 

Mnlamia 18 

Spliyrna 27 


•7 

•05 

•1 

•5 

•1 

•(I 

•01 

■0 

•() 

•;{ 

.■) 

•in; 

•1 

11 

•(5 

•1 

■oil 

■0 

•!» 

•9 

•(I 

■07 
•10 

■II 

■1 

•7 

•;; 

•0 

■1 

•oc 

■01 

■0 

•(; 
1-:! 

•4 
(•> 

•1 

•01) 

•0 

•8 

■5 

•(I 

■07 

■0 

•:{ 

•.•{ 

•1 

■10 

•;; 

•4 

•5 

•u 

■0!) 
•05 

•0 
•1 

•7 
11 

■(; 

•7 

•2 

•12 

•0 

•7 

■4 

•5 

■o;i 

•0 

•1 

■;{ 

Tlie  eh:ini]fos  whicli  ;ire  presenUHl  consist  chieHy  in  concrescence. 
This  takes  place  in  various  ways.  The  proximal  portions  more  fre- 
quently vmite  tlian  the  distal,  but  we  may  have  conci-escence  of  the 
distal  points  while  the  proximal  portions  are  separate.  The  reduction 
of  rays  is  exhibited  in  all  deoreos  from  the  slightest  shortenino-  t() 
the  extreme  degree  shown  in  PI.  LVTI,  tig.  50,  ray  0. 

It  is  perhaps  noteworthy  that  the  changes  which  would  have  suf- 
ficed to  differentiate  the  fin  of  one  species  from  another,  if  they  had 
continuously  advanced  for  a  few  generations,  are  changes  which  in 
no  slight  degree  are  now  taking  place  ln'twcen  parents  and  childi-cn. 
I  mean  changes  of  number,  segmentation,  concrcsccni'c,  and  relative 
lengths  of  parts  of  rays. 

I  exhibit  SOUK'  figures  of  the  dorsal  tins  of  Sqin/li/.^,  1*1.  LVIT, 
figs.  51-r)0,  and  PI.  LVIII,  iig.  57,  liditt,  PI.  LVIII,  tigs.  5S,  55),  and 
Mt/liohafiti,  PI.  7>VIIT,  fig.  (iO.  It  is  perfectly  certain  that  they  have 
been  derived  from  a  sei-ies  of  parallel  rays,  and  that  the  jjrincipal 
process  of  change  has  beiMi  in  tlu'  way  of  concrt'scence.  They  tell 
their  own  story  as  far  as  it  can  be  told  without  the  investigation  of 
other  closely  related  forms. 

The  last  ray  in  the  first  dorsal  of  /xa/'o,  PI.  lAIII,  tig.  5S,  is 
remarkable,  and  it  is  represented  in  the  second  doi-sal.  fig.  50,  by  a 
serii'S  of  se])arale  nodules. 


J.  K.  TJiacher — Medhin  (iiul  Paired  Fins.  291 

I  m1s(.  add  tiouivs  of  the  dorsal,  I'l.  LVIIF,  fig.  01,  and  anal,  PI. 
LIX,  lio-.  02,  of  A(-/j)enNer.  Tlu'so  arn  very  similar  to  the  simpler 
shark  dorsals.  It  will  be  iioticed  tliat  we  have  the  ])redoniinant 
division  into  three  pieces,  hul  llie  terminal  piece  is  very  shoi't. 

(Joiiiiiisioiis  rei/arditKj  McxVihh  Fins. 

'i'lie  priniortlial  median  lin-rays  in  whatever  form  they  oce\ir  are 
derivatives  from  a  serit's  of  simple  parallel  chondroid  rods,  which 
grew  up  in  the  me<lian  fold  in  total  independencte  of  the  cartilaginous 
arches  alxni'  and  Itelow  the  notochord.  These  earliest  representa- 
tives of  these  parts  weri'  irom  two  to  four  times  as  numerous  as  the 
vertebra'  opposite  them.  In  the  (inathostomi  true  hyaline  cartilage 
replaced  (he  lowei-  form  of  tissue  seen  in  Myxlne  and  Petromyzon. 

Segnu'ntation  and  c(»ncresceiice,  as  well  as  redu(!tion  in  size,  were 
common  changes  in  the  (rnathostomes,  and  here  a  division  into  three 
parts  is  the  usual  though  not    invariable  rule. 

Hence  it  is  seen  that  (iegenbaui"'s*  st:itement  that,  in  their  sinijjlest 
forni,^the  prinioidial  tin  rays  are  mere  pi-olongations  of  the  neural 
spines  is  incon-ect.  It  has  been  demonstrated  that  this  was  not  the 
earliest  foi-m.  The  l)ij)noans,  however,  seem  to  oft'er  an  example 
where  the  priim)rdial  meclian  fin-rays  are  mere  prolongations  of  the 
neui-al  spines.     They  demand  a  moment's  consideration. 

True  neural  spines  are  lirst  found  in  the  (ianoids.  They  are  absent 
in  the  Klasmobranchs  and  Agnathostomi.  PI.  LIX,  fig.  0;i  represents 
the  projection  of  a  section  of  a  vertebi-al  segment  of  Acipenser  cut 
through  the  middle  line  of  the  arch  ami  neural  spine.  .\s  the  latter 
slopes  backwai'd,  it  is  considerably  fon'shortened  in  the  figure. 

Now  the  cartilaginous  arches  spriiigiiig  from  the  sheath  of  the 
notochord  pass  upwards  to  lay  themselves  on  each  side  of  the  fibrous 
cord  />,  and  here  they  sprea<l  inward  to  meet  oiu'  another  on  the  ventral 
side  of />,  and  also  pi'olong  themselves  above  to  almost  or  quite  meet, 
and  then  they  are  followed  by  the  dorsal  spine  a,  from  which  they 
are  se])arated  by  a  segmentation. 

Now  the  cord  A,  which   is  the  same  as  the  Uyainentum  loiKjitadi- 


*  Griiiidriss  der  Vergleichenden  Anatomie,  1873,  p.  488.  Gregenbaur's  assertion 
in  the  .same  place  tliat  they  usually  correspond  in  number  to  the  vertebra?  opposite, 
is  very  strange.  We  have  already  seen  that  they  do  not  do  this  in  the  earlier  and 
more  significant  forms  ;  and  the  statement  of  Gegenbaur  would  decidedly  misrepresent 
what  we  find,  for  e-xamplc,  hi  tlie  figures  of  fish  skeletons  in  Agassiz's  PoisBons 
Fossiles. 


292  J,  K.  Thacher — Median  and  Paired  J^)'ns. 

nale  in  Cerafodus*  is  also,  without  the  slightest  doubt,  homologous 
with  the  chord  which  lies  entirely  above  the  neural  arch  in  the  Elas- 
mobranchs.  The  peculiar  fibrous  character  is  almost  exactly  the 
same  in  each.  We  have  seen  that  this  cord  in  the  sharks  is  in  all 
probability  homologous  with  the  fibrous  tatty  ridge-pole  of  the 
neural  canal  in  Petroniyzon.  Thus  while  in  the  latter  the  arches  of 
one  side  and  the  other  are  entirely  separate,  in  the  sharks  they  have 
spread  beneath  the  ligament  so  as  to  meet,  and  in  the  higher 
Gnathostomes  they  have  also  joined  above  it,  or  nearly  joined,  for 
the  origin  of  a  is  still  to  be  discussed. 

There  are  two  possibilities  with  regard  to  the  neui-al  spine  a.  Either 
it  is  formed  by  the  union  of  a  median  fin-ray  with  the  neural  arches, 
the  ray  thus  constituting  the  keystone  of  the  arch,  or  else  by  the 
union  of  the  neural  rods  from  each  side  and  their  prolongation  dorsad. 

But  the  junction  between  <i  and  h  is  quite  close ;  the  neural  spines 
correspond  in  number  and  j)osition  with  the  lateral  parts  of  the  arch  ; 
while  fig.  61  shows  conclusively  the  absolute  independence  of  neural 
spines  and  primordial  median  fin-rays. 

The  second  of  the  two  possibilities  is  then  the  true  one.  Thus 
neither  are  median  fin-rays  derived  from  neural  spines,  nor  neural 
spines,  where  they  occur,  from  primordial  fin-rays. 

But  the  cartilaginous  supports  of  the  median  told  in  the  Dipnoans 
are  very  long  and  segmented.  They  are  simply  elongated  neural 
spines  and  are  not  primordial  fin-rays  in  any  homological  sense. 
If  they  were  formed  by  the  reduction  in  number  of  the  primordial 
fin-rays  and  their  coalescence  with  the  neural  sjjines  it  is  impossible 
that  we  should  not  have  here  and  there  an  extra  one,  and  some  evi- 
dence in  the  case  of  others  of  such  a  junction.  But  there  is  nothing 
of  the  kind,  either  in  the  descriptions  of  Gtinther  in  the  case  of  Gera- 
toduSjj  or  in  those  of  Owen  J  and  Peters§  in  that  of  Protopterus  annec- 
tens.  or  in  those  of  Bischofi"||  in  that  of  Lepidosiren  paradoxa.     Gtln- 


*  Griinther's  Description  of  Ceraiodus,  Pliil.  Trans.,  vol.  elxi,  pt.  ii,  PI.  XXXVIII, 
Pigs.  3-9,  e. 

f  Phil.  Trans.,  vol.  clxi,  pt.  ii,  1871.  G-iinther,  Description  of  Oeratodu.s.  In  Giinther's 
fig.  2,  PI.  XXX,  the  proximal  joint  of  the  14tli  neural  spine  seems  to  bear  two 
' '  interneurals,"  one  orad  of  the  other.  But  as  no  notice  is  taken  in  the  text  of  this, 
which  would  be  a  very  noteworthy  fact,  if  it  were  fact,  and  as  the  description  of  these 
parts  there  given  is  such  as  would  demand  a  notice  of  this  exception,  it  is  evident 
that  it  must  be  an  inaccuracy  in  the  figure. 

:|:  Trans.  Linnean  Soc,  vol.  xviii,  pt.  iii.     Owen,  Description  of  Lepidosiren  annedens. 

§  Miiller's  Archiv.,  1845.  Peters,  Ueber  einen  dem  Lepidosiren  annectens  verwandten, 
Fiach  von  Quellimane. 

II  Ann.  Sc.  Nat.,  xiv,  1840.     Bischoif,  Sur  le  Lepidosiren  iiaradoxa. 


J.  K.  Thiieher — Median  and  Paired  Fins.  298 

tiler's  denoraiiiation,  tlu'ii,  of  tlie  ultiniato  and  ])eiiultimate  joints  of  the 
neural  S])ines  of  Ceratodas  as  "  interneural  first"  and  "  interneural 
second,"  is  ill  chosen,  and  rests  on  a  mistake  in  homology.  That 
great  genetic  group,  then,  consisting  of  Dipnoi,  Amphibia  and  Am- 
niota,  seems  to  have  entirely  lost  those  primordial  median  fin-rays 
which  appeared  so  early  and  are  found  even  in  Mxjxine. 

Limb-skeleton  of  Air  breathing  Vertebrata. 

In  1864,  Gegenhaur*  set  forth  the  splendid  results  of  a  widely 
extended  investigation  of  the  limb-skeleton  of  the  air-breathing 
vertebrates.  Herein  was  established  the  typical  form  of  these  parts 
for  this  large  gi'oup,  consisting  of  Amphibia  and  Amniota.  Inasmuch 
as  there  is  no  doubt  of  the  natural,  that  is  the  genetic,  character  of 
this  group,  and  inasmuch  as  it  is  marked  out  from  all  other  vejte- 
biates  by  the  development  of  a  fenestra  ovalis  and  the  modification 
of  the  proximal  part  of  the  second  post-oral,  or  hyoid,  arch  into  a 
stapes  in  connection  therewith,  I  ventui'e  to  use  the  name  Stapedifera 
in  place  of  the  circumlocutory  air-breathing  Vertebrates.  For  the 
Stapedifera,  then,  the  typical  limb-skeleton  was  established ;  typical 
in  the  sense  of  the  older  anatomists,  as  that  ideal  form  from  Avhich 
we  could  in  our  minds  easily  derive  the  various  actual  forms  now 
living  ;  but  typical  also  in  the  newer  sense,  as  that  actual  form,  the 
limb-skeleton  of  the  latest  common  ancestors  of  all  Stapedifera,  from 
which  have  been  developed  the  corresponding  parts  in  all  living 
Stapedifera. 

The  same  form  belongs  to  both  fore  and  hind  limbs.  Using  the 
names  applicable  to  the  former,  we  have,  as  is  well  known,  humerus, 
radius  and  ulna,  radiale,  intermedium  and  ulnare,  a  centrale,  and 
then  set  around  these,  five  cai'palia  followed  by  their  metacarpals 
and  phalanges.  Moreover,  the  strong  suspicion  of  the  double  nature 
of  the  centrale,  as  evidenced  in  the  descriptions  of  Cryptobranchns 
JaponiGus.\  by  Schmidt,  Goddard,  and  J.  Van  der  Hoeven,  is  later, 
1865,  confirmed  by  the  careful  observations  and  clear  presentation 
of  the   anatomy  of  that  animal  by  Hyrtl.J;     The  Ichthyosaurs§  and 

*  Gegenbaur,  Untersuchungen  zur  vergleichenden  Anatomie  der  Wirbelthiere, 
Hft.  1,  Carpus  imd  Tarsus. 

f  Gegenbaur,  Unters.,  Hft.  1,  p.  57. 

\  Hyrtl,  Schediasma  anatomicum.  1865.     Gegenbaur,  Unters.,  Hft.  2,  p.  165. 

§  Gegenb.,  Unters.,  Hft.  2,  p.  165,  and  Jena  Zeitschr.,  Bd.  v,  Hft.  2,  1870.  Gegen- 
baur, Ueber  das  Gliedmaassenskelet  der  Enaliosaurier.  In  this  last  a  furtlier  modifi- 
cation is  made  in  tlie  recognition  of  the  pisiform  as  the  remains  of  a  sixtli  row,  an(] 
as  being  an  essential  part  of  the  carpus  and  not  merely  a  sesamoid  bone. 


294  ./.  K.  Thacher — Median  and  Paired  Fins. 

Plesiosaurs  give   too  their    unambiguous   evidence   in   the  same  di- 
rection. 

This  limb  of  the  latest  common  ancestors  of  the  Stapedifera,  this 
typical  limb  of  that  group,  has  been  named  by  Huxley,  chiropter- 
ygium*  and  the  term  will  be  found  convenient. 

The  (Jhiropterygium  and  the  Fins  of  Fishes. 

The  homology  between  the  paired  fins  of  fishes  and  the  limbs  of 
Stapedifera  has  long  been  recognized  ;  but  the  special  homologies 
of  the  skeletal  parts  of  each  has  been  the  subject  of  much  controversy. 
For  a  historical  sketch  of  the  various  divergent  opinions  endorsed  by 
the  highest  authorities  I  must  refer  to  the  second  volume  of  Gegen- 
baur's  Untersuchungen. 

Two  pairs  of  limbs  are  found  throughout  the  great  genetic  group  of 
the  Gnathostomi.  The  chiropterygium  having  been  established,  the 
determination  of  that  earlier  form  typical  for  all  the  Gnathostomi 
became  a  more  pressing  question. 

To  an  answer  to  this  question  the  investigations  of  Gegenbaur  now 
begin  to  lead. 

The  first  part  of  the  second  volume  of  the  Untersuchungen  dis- 
cusses the  shoulder  girdle,  and  the  result  is  that  we  are  now  able  to 
trace  clearly  and  surely  the  primordial  shoulder  girdle,  the  scapulo- 
coracoid,  throughout  the  Vertebrata.  We  are  no  longer  in  doubt  as 
to  what  part  of  the  fish  fin  and  girdle  corresponds  to  limb  and  what 
to  girdle  of  the  Stapedifera.  The  results  of  Ge'genbaur's  work  with 
which  we  are  hei'e  concerned  were  confirmed  by  the  later  but  inde- 
pendent researches  of  Parker.f 

Development  of  the  Archipterygimn,  Tlieory. 

This  preliminary  question  having  been  satisfactorily  answered,  the 
derivation  of  the  chiropterygium  is  next  attempted. 

The  second  half  of  the  second  volume  of  the  Untersiichungen  (1865) 
takes  up  the  pectoral  fin  of  fishes.  Quite  a  number  of  very  excellent 
figures  of  numerous  Elasmobranchs,  Ganoids  and  Teleosts  are  given, 
and  the  limb  skeleton  of  Protopteras  is  discussed.     The  conclusions 

drawn  are  as  follows : 

We  may  take  as  the  most  generalized  form  of  limb  that  of  the 
Elasmobranchs,  where  its  various  parts  are  most  plainly  presented  in 


*  Proc.    Zool.   Soc.    London,    IS?*!,  pt.   i,    p.   56.       T.   H.    Huxley,   On    Ctratodus 
Forsteri. 

•j-  Parker,  Slioulder-girdle  and  Sternnni.     Kay  Soc,  IMGS. 


J.  K.  Tliaeher — Median  and  Paired.  Fins.  295 

the  rays.  It  is  divided  into  three  parts,  Propterygium,  Mesoptery- 
gium  and  Meta])terygium.  Each  of  tliese  consists  of  a  basale,  vvliich 
articulates  Avith  the  shoulder  girdle,  and  a  number  of  rays  set  on  its 
edge. 

The  fin  of  Protopteriis  is  derived  from  this  by  the  destruction  of  the 
pro-  and  mesopterygium.  The  metapterygiiim  is  hei'e  represented  by 
the  long  articulated  rod,  Avhich  alone  remains  in  Liepidosiren paradoxa . 
The  row  of  cartilages  along  its  sides  are  the  metapterygial  rays. 

In  the  Ganoids,  Polypterns  alone  has  the  three  divisions  repi'e- 
sented.  In  this,  neither  metapterygium  nor  propterygium  bears  rays. 
These  are  confined  to  the  mesopterygium,  which  is  excluded  from  the 
articulation  with  the  shoulder  girdle. 

In  the  other  Ganoids  the  propterygium  fails.  Between  the  mesop- 
terygium and  metapterygium  a  number  of  rays  are  brought  into 
articulation  with  the  shoulder  girdle,  resembling  what  is  seen  in  some 
of  the  Rays. 

The  Teleosts  in  the  main  resemble  this  second  group  of  Ganoids. 

The  chiropterygium  is  derived  from  the  metapterygium  alone,  and 
thus  resembles  the  limb  of  Protopterus.  The  fore  limb  will  serve  as 
an  example.  The  Stammreihe  or  hasale  nietapterygii  is  presented 
by  the  humerus,  radius,  radiale,  carpale  radii,  the  metacarpal  and 
phalanges  of  the  thumb.  The  other  bones  are  the  rays  belonging  to 
this,  and  their  arrangement  will  be  best  understood  by  looking  at  the 
Ichthyosaurtis  limb,  fig.  70.  In  1870,*  Gegenbaur  published  his 
explanation  of  the  liml)  of  the  Enaliosaurs.  The  unbroken  lines  in 
fig.  70  of  Ichthyosaurus  exhibit  his  view  of  the  relations  of  the  fin 
with  that  of  fishes.  This  may  be  regarded  as  closing  the  first  stage 
of  the  development  of  the  theory  in  Gegenbaur's  publications. 

The  second  immediately  opens.  For  in  the  next  numberf  of  the 
Jena  Zeitschrift  there  appears  an  extended  article  on  the  ventral  fins 
of  Elasmobranchs.  The  pre\'ious  view  is  modified  as  follows.  The 
fin-skeleton  of  the  latest  common  ancestors  of  all  Gnathostomes,  is 
represented  pure  and  simple  in  the  fore  limb  oi  Protopterus  a nnectens^ 
and  with  only  slight  modification  in  the  ventral  fins  of  Elasmobranchs. 
It  now  has  a  name  given  to  it.  It  is  called  archipterygium.  There 
is  a  limb  gii-dle,  complete  ventrad.    On  each  side  is  articulated  to  this 

*  Jenaische  Zeitschr.,  Bd.  v,  Hft.  .S.  Gegenbaur,  Ueber  das  Gliedmaassenskelet 
der  Enaliosaurier,  Feb.,  1870. 

f.Ten.  Zeitschr.,  Bd.  v,  Hft.  4.  Gegenbaur,  Ueber  der  Gliedmaassen  der  Wirbel- 
thiere  im  AUgemeinen  und  der  Hintergliedraaassen  der  Selachier  insbesondere,  May, 
1870. 


296  '/  K.  Thacher — Median  and  Paired  Fins. 

the  stem-row  {Stamm-relhe) ,  a  long  taperiug  many-jointed  cartilaginous 
rod  which  bears  on  the  outer  side  a  series  of  rays.  Tliis  evidently 
calls  for  no  change  of  view  regarding  the  Enaliosaurs  or  Stapedifera. 
But  the  fin-skeleton  of  iishes  exhibits  everywhere,  except  in  Pro- 
topterus  and  Sct/mnus,  a  slipping  off  of  the  rays  from  the  stem-row" 
and  their  articulation  with  the  girdle,  and  very  commonly  their  artic- 
ulation with  one  another  and  considerable  fusion  (concrescence). 

Still  another  change  awaits  the  primordial  limb,  even  the  named 
archipterygium.  In  1871,  Gtinther*  published  his  description  of 
Ceratodus.  Here  the  stem-row  has  a  series  of  rays  down  each  side. 
The  archipterygium  is  modified  to  accord  with  this  in  the  Jena 
Zeitschrift  published  x\pril  22,  1872,f  where  Gegenbaur  adopts  the 
"  Biseriale  Archipterygium''''  as  the  parent  form,  and  attempts  to 
show  that  there  are  some  traces  of  the  median  row  of  rays  in  the 
pectoral  fins  of  some  Elasmobranchs.  With  the  exception  of  Cerato- 
dus and  the  questionable  exception  of  these  Elasmobranch  pectorals, 
the  biserial  has  been  everywhere  reduced  to  the  uniserial  form,  and 
still  further  reduced  as  heretofore  explained. 

In  the  third  volume  of  the  Untersuchungen,  dated  May,  1872,  a 
suggestion  J:  is  made  of  the  possible  origin  of  the  Archipterygium  and 
the  limb-girdles.  They  are  assimilated  to  tlie  branchial  arches  and 
their  diverging  rays,  where  rays  move  up  upon,  and  articulate  with, 
the  longest  middle  ray.  It  is  but  justice  to  say  that  the  suggestion  is 
a  little  vaguely  and  liesitatingly  made. 

In  confirmation  of  Gcgenbaur's  views,  Bunge,§  in  1874,  published  a 
further  investigation  of  the  pectoral  fin  of  Elasmobranchs,  showing  a 
number  of  rays  which  might  be  regarded  as  median,  in  several  species 
not  examined  by  Gegenbaur.  Finally,  in  1876,  Huxley ||  took  up  the 
question,  and,  wliile  he  accepted  the  archipterygium,  he  modified  the 
interpretation  of  a  large  number  of  the  forms. 

*Proc.  Roy.  Soc,  1871,  p.  378,  and  more  fully,  with  a  figure  of  the  fin-skeleton,  in 
Ann.  and  Mag.  of  Nat.  Hist.,  March,  1871.  To  these  Gegenbaur  refers,  Jen.  Zeitsclir., 
Bd.  vii,  Hft.  2,  p.  132,  note.  But  a  much  fuller  description  is  given  by  Giinther,  Phil. 
Trans.,  vol.  clxi,  pt.  ii,  pp.  511-572.     This  vs^as  pubhshed  early  in  1872. 

f  Jen.  Zeitschr..  Bd.  vii,  Hft.  2,  pp.  131-141.  Gegenbaur,  Ueber  das  Archip- 
terygium. 

:};  Gegenbaur,  Unters.,  Hft.  III.     Kopfskelet  der  Selachier,  p.  181,  note.    1872. 

§  A.  Bunge,  Jena.  Zeitschr.,  Bd.  8,  Hft.  2,  1874.  Ueber  die  Nachweisbarkeit  eines 
biserialem  Archipterygium  bei  Selachiern  und  Dipnoern.  Bunge  also  calls  attention 
to  the  fact  that  the  fringing  rays  in  Protoptems  a-i,nectens  are  on  the  median  (i.  e.,  ven- 
tral,) side  of  the  axis,  and  not,  as  in  Elasmobranchs,  on  the  lateral  (i.  e.,  dorsal,)  side. 

II  T.  H.  Huxley,  Proc.  Zool.  Soc.  Lon.  for  1876,  PI.  1.     On  Ceratodus  Forsteri. 


J.  K.  ThacJier — Median  and  Paired  Fins.  297 

Most  of  the  inoditications  introduced  by  Huxley,  though  perhaps 
not  all,  spring  from  a  question  which  is  independent  of  any  theory 
with  regard  to  the  skeleton,  archipterygium  or  other,  but  which, 
superior  to  them,  must  determine  the  application  of  them  to  the 
passage  fi-om  the  tisli  limb  to  that  of  Stapedifera. 

If  an  Elasmobranch  pectoral  fin,  for  example,  of  Mustelus,  be  re- 
moved and  laid  on  the  corresponding  hand,  with  the  propterygial  edge 
toward  the  thumb,  and  the  metapterygial  edge  toward  the  little 
linger,  then  the  ventral  surface  of  the  fin  will  look  in  tlie  same  direc- 
tion as  the  palmar  surface  of  the  hand.  But  if  it  be  turned  over  so 
that  the  metapterygial  edge  corresponds  to  the  thumb  and  the  prop- 
terygial to  the  little  finger,  then  the  dorsal  surface  of  the  fin  will 
correspond  to  the  palmar  surface  of  the  hand. 

One  or  the  other  of  these  views  must  be  taken.  There  is  no  third 
possible.  Huxley  takes  the  first,  Gegenbaur  the  second.  This,  how- 
ever is  no  new  question  and  no  new  difference  of  opinion.  Cuvier, 
following  Bakker,  named  the  two  ossifications  of  the  scapulo-coracoid 
which  are  so  generally  found  in  osseous  fishes,  radius  and  ulna. 
Owen  simply  reversed  this  nomenclature  and  Mettenheimer  followed 
him.  The  question  was  the  same  as  now  respecting  the  homologies 
of  faces  and  edges  of  fin  and  limb.  On  the  one  side,  then,  we  have 
Bakker,  Cuvier  and  Huxley  ;  on  the  other,  Owen,  Mettenheimer  and 
Gegenbaur.  The  weight  of  evidence  seems  to  me  to  be  in  favor  of 
the  view  entertained  by  the  latter  group,  namely,  that  the  metaptery- 
gial edge  of  the  fish  fin  corresponds  with  the  radial  or  thumb  side  of 
the  hand,  and  consequently  that  the  dorsal  surface  of  the  fish  fin  is 
the  palmar  (or  plantar)  surface.     But  I  have  no  new  facts. 

By  reviewing  Gegenbaur's  work  it  will  be  seen  that  this  theory  of 
his  rests  upon  the  form  of  the  limbs  in  the  Elasmobranchii  and 
Dipnoi.  In  the  former  grouj)  it  is  the  hind  limbs  which  furnish 
nearly  all  the  evidence.  The  fore  limbs  (pectorals)  are  brought  in 
merely  to  testify  to  the  hiserial  character  of  the  archipterygium,  of 
which  no  Elasmobranch  ventral  gives  a  sign.  That  is  to  say,  the  ven- 
trals  having  testified  to  the  archipterygium,  and  that  having  been 
accepted,  the  pectorals  find  use  for  themselves  in  showing  thai  it 
was  fringed  down  tlie  median  as  well  as  the  lateral  side.  If  then  the 
same  form  of  limb  is  found  in  Elasmobranch  and  Dipnoan,  the  same 
form  was  undoubtedly  possessed  by  their  common  ancestors.  But  as 
their  common  ancestors  were  also  undoubtedly  common  ancestors  of 
all  Gnathostomes,  therefore  all  Gnathostome  limbs  must  have  been 
derived  from  this  form. 

Trans.  Conn.  Acad.,  Vol.  III.  38  February,  1877. 


298  J.  K.  Thacher — Median  and  Paired  Fins. 

The  testimony  of  the  Ganoids  and  Teleosts  seems  to  me  to  be 
somewhat  adverse  to  the  theory.  Again  it  is  impossible  to  think 
that  that  of  the  Stapedifera  can  be  very  clearly  in  its  favor,  when 
Huxley,  while  accepting  the  archipterygium  as  the  parent  form, 
gives  an  explanation  of  the  cliiropterygium  entirely  distinct  from  and 
utterly  inconsistent  with  that  of  Gegenbaur. 

Any  opinion  adverse  to  the  archipterygium  theory  will  have  diffi- 
culty in  maintaining  itself,  so  long  as  it  does  not  show  that  the 
resemblance  between  the  fins  of  sharks,  and  those  of  Dipnoi  is  a 
merely  superficial  one,  and  is  not  able  to  suggest  how  a  certain  show 
of  resemblance  might  have  arisen  in  two  entirely  distinct  and  different 
series  of  developments. 

Another  View  of  the  Origin  of  Vertebrate  Limbs. 

Into  competition  with  this  theory,  which  sees  in  the  fin  of  Cera- 
todus  that  from  which  all  other  limbs  have  been  derived,  I  bring  a 
second  which  sees  in  the  same  only  a  special  development  peculiar 
to  the  Dipnoi.     It  is  this. 

As  the  dorsal  and  anal  fins  ^cere  specializations  of  the  median  folds 
of  Amphioxus^  so  the  paired  fins  were  specializations  of  the  tioo  lateral 
folds  which  are  supplementary  to  the  median  in  completing  the  cir- 
cuit of  the  body.  These  lateral  folds,  then,  are  the  homologues  of  the 
Wolffian  ridges,  in  embryos  of  higher  forms.  Here,  as  in  the  median 
fins,  there  were  formed  chondroid  and  finally  cartilaginous  rods. 
These  became  at  least  twice  segmented.  The  orad  ones,  wuth  more  or 
less  concrescence  proximally,  were  prolonged  inwards.  The  cartilages 
spreading  met  in  the  middle  line,  and  a  later  extension  of  the  carti- 
lages dorsad  completed  the  limb  girdle. 

If  now  we  seek  to  determine  the  form  of  limb  for  the  Protognathos- 
tomi,  that  is  to  say,  for  that  time  for  which  the  archipterygium  in 
its  entii'ety  is  proposed,  we  should  propose  this. 

TTie  limbs  of  the  Protognathostomi  cimsisted  of  a  series  of  parallel 
articulated  cartilaginous  rays.  They  may  have  coalesced  somewhat 
proximally  and  orad.  In  the  ventral  pair  they  had  extended  them- 
selves mesiad  until  they  had  nearly  or  quite  met  and  formed  the  hip 
girdle.  They  had  not  here  extended  themselces  dorsad.  In  the  pec- 
toral limb  the  same  state  of  things  prevailed,  but  was  carried  a  step 
further,  namely,  by  the  dorsal  extension  of  the  cartilage  constituting 
the  scapidar  portion,  thus  more  nearly  forming  a  ring  or  girdle. 

This  theory  naturally  diA'ides  itself  into  two  parts,  namely,  the 
derivation  of  the  Gnathostome  limb  from  a  series  of  sim})le  parallel 


J.  K.  Thacher — Median  and  Paired  Fins.  299 

cartilages,  and  the  derivation  of  tlie  latter  from  the  lateral  folds  of 
Amphioxns. 

Though  the  last  mentioned  portion  of  the  theory  would  derive 
considerable  strength  from  the  establishment  of  the  first,  it  is  not  a 
necessary  consequence  of  it,  and  the  first  might  be  true  even  if  the 
last  were  false.     If  the  last  be  true,  of  course  the  first  must  be  true. 

The  establishment  of  the  derivation  from  the  lateral  folds  of 
Ainphioxus  is  made  difficult  from  the  al)senee  of  limbs  or  anything 
representing  them  in  the  two  groups  which  (in  a  sense)  stand  between 
Amphioxus  and  the  Elasmobranchs,  namely,  the  Myxinoids  and 
Lampreys. 

As  will  be  seen,  it  assumes  the  essential  correctness  of  Huxley's 
suggestion  with  regard  to  the  relation  between  the  folds  which  grow 
down  to  inclose  the  atrial  cavity  of  Amphioxus  and  the  body  walls 
of  higher  vertebrates.  But  it  is  equally  consistent  with  Huxley's* 
entire  suggestion,  as  put  forth  by  him,  or  with  Ray  Lankester'sf 
modification  of  it. 

On  the  other  hand,  it  is  inconsistent  with  Kowalewsky'sJ  view  of 
the  homology  between  these  and  opercular  folds.  This  must  perhaps 
be  consideied  still  an  open  question,  though  Rolph's§  arguments  on 
the  other  side  seem  to  me  of  much  less  weight  than  they  do  to 
Semper.  II 

Yet  even  if  this  homology  with  the  lateral  folds  should  have  to  be 
giVen  up  (the  embryology  of  the  Marsipobranchs  will  throw  consid- 
erable light  on  it),  the  very  frequent  occurrence  of  the  formation  of 
external  lateral  folds  parallel  to  the  axis  of  the  body  in  the  bilateral 
animals  in  general  and  in  the  Vertebrates  in  particular,  renders  it 
quite  possible  that  the  paired  fins  may  have  had  a  similar  origin. 
At  present,  however,  I  am   strongly  of  the  opinion  that  they  are 


*  Joum.  of  Linn.  Soc,  vol.  xii,  No.  59,  May,  1875.  Huxley,  Classification  of  the 
Animal  Kingdom. 

f  Quarterly  Journ.  of  Micr.  Sc,  New  series,  No.  59,  July,  1875.  Ray  Lankester, 
New  Points  in  the  Structure  of  Ampliioxus. 

X  Mem.  St.  Petersb.  Acad.,  VII  Series,  tome  xi.  No.  4,  1867.  A.  Kowalewsky, 
Entwickelungsgeschichte  des  A  mphioxus  lanceolatus. 

§  Sitzungsberichte  der  Naturforschenden  Gesellschaft  zu  Leipzig.  .Tahrg.  II,  No.  1, 
Jan.  29,  1875.  Rolph.  Unters.  viber  den  Ban  des  Amphioxus  lanceolatus.  See  also 
for  a  complete  account  of  his  investigations,  under  .,he  same  title,  Morph.  Jahb.,  Bd., 
ii,  Hft.  1,  1876. 

II  C.  Semper,  Die  Verwandtschaftsbeziehungen  der  gegiiederten  Thiere,  1875,  p. 
317.  (Sep.  Abdr.  aus  Semper:  Arbeiten  a.  d.  Zoolog-zootom  Institut  zu  Wurzburg, 
Bd.  II). 


300  J.  K.  Thaoher — Median  and  Paired  Fins. 

derived  directly  from  the  lateral  folds  of  Amphioxus.  These  in  their 
turn  may  be  referred  to  a  reduplication  of  the  process  which  has 
already  formed  the  atrial  space,  but  which  is  not  carried  so  far  here, 
in  the  lateral  folds. 

Ventral  F'm  of  Aci2')enser. 

The  ventral  fin  of  a  young  specimen  of  Acijyenser  hreiiirostris  is 
exhibited  in  PI.  LIX,  figs.  64  and  05.  The  fin  of  one  side  is  separate 
from  that  of  the  other,  no  synchondrosis  uniting  the  two  halves  of 
the  girdle.  But  the  part  J>  approaches  closely  its  fellow.  The  same 
separateness  of  the  two  sides  obtains  in  the  shoulder  girdle.  The 
composition  of  the  fin  is  peifectly  evident.  Beginning  at  the  aborad 
end  of  the  row,  we  have  first  three  separate  and  parallel  rays.  The 
proximal  joints  increase  in  length  from  the  first  to  the  last  of  the 
three.  In  the  remaining  rays  these  basal  joints,  increasing  still  moi'e 
in  length,  have  united  with  each  other  to  form  the  large  pelvic  piece 
ab.  The  composite  nature  of  this  is  confirmed  by  the  groovings  of 
the  surface,  which  extend  about  a  centimeter  before  they  finally  fade 
out. 

The  iliac  process,  «,  is  half  a  centimeter  high. 

In  fig.  64  the  proximal  joint  of  the  penultimate  ray  grows  up  a  little 
under  the  last  ray,  in  the  manner  familiar  in  the  median  fins.  It  does 
not  happen  to  occur  in  the  fin  of  the  other  side,  fig.  65. 

The  predominant  three-fold  division  obtains.  But  the  penultimate 
ray  in  fig.  64  has  a  tip  or  an  extra  segmentation,  and  c  is  without 
the  distal  segmentation. 

The  breadth  and  the  outline  of  c  raises  the  suspicion  of  its  double 
character. 

I  have  had  >io  opportunity  of  examining  other  Ganoid  fins,  and 
this  one  of  Aci2^enser  seems,  on  the  whole,  that  which  most  nearly 
approaches  the  parent  form  of  the  Gnathostomes.  But  while  in  the 
independence  of  the  two  sides,  in  the  separateness  of  the  I'ays,  and 
the  simple  segmentation,  it  gives  us  the  early  form  more  complete 
than  is  elsewhere  found,  in  the  number  of  rays  and  hi  the  absence  of 
the  iliac  process  the  shark  ventrals  are  less  advanced. 

Elasmohraiich  YentraU. 

We  now  turn  to  the  derivation  of  the  ventral  fins  of  sharks,  one  of 

the  two  abutments   of  the  Inroad  S{)an   of  the  archiptcrygiuru  theory. 

The  series  of  steps  by  which  I  conceive  them  to  have  been  derived 


J.  K.  Thaeher — Median  and  Paired  Finn. 


301 


from  the  row  of  ]>arallel  rays  is  presented  in  woodcuts  A,  B,  C  and  D. 

The  kind  of  'cliange  invoked  is 
simply  coneresence,  with  scmie 
spreading  of  the  cartilage.  The 
former  of  these  processes  is  abun. 
dantly  shown  in  the'  case  of  the 
median  tins,  while  something  of  the 
latter  process  is  seen  in  PI.  LI,  figs. 
12,  18,  14,  15;  PI.  LIII,  fig.  27; 
PI.  LVI,  fig.  46  ;  PI.  LVII,  fig.  49. 
And  it  is  noteworthy  that  here  the 
rays  which  jn'olong  themselves  prox- 
imally  are  the  orad  ones,  just  as  they 
are  in  the  ventral  fins.  As  for  the 
concrescetice,  this  has  been  carried 
much  farther  in  the  dorsal  ^n^  oi  ^Sq^la- 
lusAmericanus,3ryliobatis  and  Raia 
levis  than  it  has  in  the  shark  ventrals. 
It  is  barely  possible  that  the  definiteness  and  constancy  of  the  concres- 
cence in  the  latter  may  be  in  whole  or  in  part  determined  by  the 
copulatory  function  of  the  last  part  of  the  fin  in  male  Elasmobranchs. 
While  the  derivation  of  the  ventral  fins  is  thus  easy  from  a  series  of 
parallel  cartilages,  we  find  much  greater  difficulty  in  the  ease  of  some  of 
the  median  fins,  in  Raia  levis,  for  example,  which  is,  unless  my  own 
preconceptions  deceive  me,  a  far  better  case  of  a  biserial  archiptery- 
gium  than  any  furnished  in   the  paired   fins,  aside  from  Ceratodics. 

C 


Indeed  I  may  state  that  the  origin  of  this  i)aper  lay  in  an  observation 
of  a  fin  of  another  species  of  Haia,  not  however  well  enough  preserved 


302  J.  K.  Thaeher — Median  and  Paired  Pins. 

for  drawing.  The  very  striking  similarity  to  the  uniserial  archip- 
terygiuni  raised  the  question  whether  the  median  fins,  at  any  rate  the 
dorsal  and  anal  fins,  might  not  have  arisen  from  the  same  archiptery- 
ginm.  The  result  of  my  investigations  was  a  decided  negative. 
It  has  been  absolutely  proved  that  they  did  not  so  originate,  and 
the  way  in  which  they  did  originate  has  been  clearly  shown. 

While  then,  on  the  one  hand  it  has  been  shown  that  the  develop- 
ment of  a  pair  of  fins,  whoso  skeleton  consists  of  a  series  of 
parallel  rays  clothed  on  each  side  with  a  layer  of  muscle,  as  a 
specialization  of  the  lateral  folds  (raetapleura  of  Ray  Lankester)  of 
AniphioxHs,  contains  no  steps  which  have  not  been  taken  in  the  same 
animals  in  the  case  of  the  median  fins,  so  also  it  has  been  shown  that 
the  development,  of  the  ventral  fins  and  the  pelvic  girdle  of  sharks 
from  such  a  series  exhibits  no  processes  or  kinds  of  change  which  are 
not  also  exhibited  in  the  median  fins  of  those  same  fishes.  When  we 
contrast  the  changes  from  a  series  of  parallel  rays  to  the  completed 
ventral  fin  of  the  shark,  as  it  has  been  given  above,  with  the  changes 
which  Gegenbaur  supposes  to  have  made  it  out  of  the  archiptery- 
gium,  namely,  the  stripping  ofi"  of  every  one  of  the  median  rays,  for 
no  sign  of  them  is  ever  found  in  the  ventral  fins  aside  from  the  Dipnoi, 
and  the  slipping  off  of  the  orad  portion  of  the  rays  to  immediately 
articulate  with  the  shoulder  girdle,  I  hardly  think  that  those  changes 
of  his  will  appear  so  well  evidenced  as  these  changes  which  I  believe 
to  have  taken  place.  And  when  the  utter  darkness  that  covers  the 
development  of  the  arehipterygium  itself  (for  it  does  not  seem  fair  to 
the  arehipterygium  to  make  much  account  of  the  suggestion  of 
Gegenbaur  respecting  the  branchial  arches,  Unters.,  Hft.  iii,  p.  181, 
note)  is  contrasted  with  the  familiar  changes  which  would  have 
brought  these  Selachian  fins  out  of  the  lateral  folds  Ainphioxus,  I 
hardly  think  the  advantage  can  lie  with  the  arehipterygium. 

Homodynamism  of  Median,  and  Paired  P'ins.* 

Let  us  compare  the  ventral  with  the  dorsal  fins,  say  in  Mustelus 
cams. 

*  Since  this  paper  was  written,  I  have  found  a  paper  of  Humphrey's  on  the  Homo- 
logical  Relations  of  Mesial  and  Lateral  Fins  of  Osseous  Fishes,  Journ.  of  A_nat.  and 
Phys.,  Nov.,  1870.  Here  a  comparison  between  the  fins  in  question  is  made  in  the 
case  of  the  Pike,  and  the  "  Iliac  "  or  "  Pubic  "  bones  in  osseous  fishes  are  assimilated 
to  the  interneural  spines  or  to  the  prominal  part  of  them.  Goodsir  had  made  some 
earlier  comparisons  without  valuable  result.     See  Anatomical  Memoirs,  vol.  ii,  p.  lOtJ. 


J.  K.  Thdcher — Median  and  Paired  Fins.  303 

In  each  there  is  a  hiyer  of  muscle  ou  each  side  of  the  cai'tilaginous 
skeleton  ;  this  flat  mass  is  in  each  divided  into  separate  muscles  by 
septa  running  from  between  the  skeletal  rods  straight  to  the  integu- 
ment, in  the  way  exhibited  in  PI,  LIX,  fig.  66 ;  in  each  these  muscles 
develop  a  tendon  in  their  middle  plane  parallel  to  the  sides  of  the 
fin ;  this  is  inserted  in  the  fascia  over  the  terminal  cartilages  where 
the  horny  fibers  begin.  These  last  are  the  same  in  nature  and 
arrangement  in  each. 

The  skeletal  elements  remain  (see  PI.  LIX,  iig.  67).  We  have  a 
short  terminal  piece  in  each,  then  comes  a  longer  middle  piece.  There 
is  left  in  the  median  fin  a  proximal  row  of  cartilages,  for  the  most 
part  separate,  which  are  again  much  shorter  than  the  middle  pieces. 
In  the  ventral  fin  the  solid  basale  metapterygii  and  a  half  of  the  girdle 
correspond  to  these  in  every  particular,  except  in  not  being  of 
separate  rays.  The  similarity  between  the  two  fins  is  complete  except 
in  a  single  particular.  And  that  exception  would  be  removed  by  a 
process  which  is  familiar  in  both,  namely  concrescence.  Even  as  they 
stand,  I  think  that  a  ventral  tin  with  one  half  the  girdle  resembles  the 
dorsal  more  than  it  does  the  pectoral. 

A  certain  amount  of  similarity  warrants  us  in  inferring  an  earlier 
state  when  the  similarity  was  greater.  It  has  been  proved  that  at  that 
earlier  time  the  median  fins  were  composed  of  separate  rays.  The 
greater  similarity,  then,  can  only  be  attained  by  the  resolution  of  the 
basale  metapterygii  into  its  component  parts. 

In  the  Elasmobranchs,  as  is  well  known,  the  primordial  fin-skeleton 
is  supplemented  in  both  median  and  paired  fins  by  the  well  kno%vn 
horny  fibers.  In  the  higher  fishes  these  are  replaced  by  the  dermal 
rays.  The  presence  of  horny  fibers  in  the  adipose  fin  of  the  salmon, 
shows  that  the  horny  fibers  were  the  earlier  form.  Therefore  the 
same  changes  have  been  taking  place  in  the  median  and  j)aired  fins 
at  the  same  time.  The  same  general  result,  i.  e.,  of  concomitant  varia- 
tion in  median  and  paired  fins  is  confirmed  in  the  sub-groups  of 
Elasmobranchs,  with  regard  to  minor  changes  in  the  primordial 
skeleton. 

The  homodynamism  of  median  and  paii'ed  fins  comes  out  strikingly 
in  Centrlna  Salvkmi.  Here,  according  to  descriptions,  a  fold  of  skin 
is  raised  along  the  median  line  of  the  back,  recalling  the  early 
continuous  fold  of  skin  along  the  back  in  ^iniphloxus.  But  similarly 
there  appear  two  folds  of  skin  along  the  sides,  recalling  the  continuous 
lateral  folds  of  Amphioxus.  It  is  at  once  a  proof  of  the  homodynam- 
ism of  the  two,  and  a  confirmation  of  the  views  here  presented  of 
their  orisjin. 


304  J.  K.  Thacher — Median  and  Paired  Fins. 

■X  llie  Dlpnoau  Fin. 

In  the  Teleosts  and  Ganoids,  which  are  in  a  sense  intermediate 
between  the  Dipnoi  and  Elasrnobranehii,  the  limb  skeleton  has  been 
comparatively  little  modified  from  the  form  in  this  paper  set  forth  as 
the  typical  limb  skeleton  of  (Tnatliostomi.  JSeurcely  any  other  pro- 
cesses than  reduction  of  the  number  of  rays  and  concrescence  are  con- 
cerned. 

Now  in  the  fin  of  Ceratodns  the  archipterygium  form  has  certainly 
been  developed,  and  if  tlie  previous  views  be  correct,  it  has  been 
developed  from  this  series  of  parallel  rays. 

Gilnther*  has  suggested  one  way,  and  Gegenbaurf  another,  in 
which  a  row  of  parallel  rays  might  transform  themselves  into  an 
archipterygium  form.  But  it  is  possible  that  these  fringing  rays  are 
new  developments.  They  look  very  much  like  it  in  Protopterus. 
PetersJ  has  called  attention,  in  this  connection,  to  the  similar  struc- 
ture of  the  dorsal  finlets  of  Polyptenis,  and  these  might  throw  some 
light  on  the  subject.  For  myself,  I  am  strongly  inclined  to  suspect 
that  the  three  portions  of  the  second  piece  of  the  limb  of  Ceratodus^ 
which  Gilnther  describes,  indicate  three  fin-rays,  and  that  the  feather- 
ing of  one  of  these  is  a  later  development.  The  fact  that  Huxley 
could  find  no  sign  of  division  in  his  specimens  seems  of  little  weight  in 
view  of  the  complete  fusion  which  Ave  know  takes  place  here  and  there 
in  median  fins. 

The  Limh  of  Stapedifera. 
PI.  LX,  fig.  70  {Ichthyoaauni.s,)  exhibits  my  view  of  the  composi- 
tion of  the  limb  of  air-breathing  vertebrates.  The  dotted  lines  indi- 
cate the  separate  rays  of  which  it  is  composed.  But  there  are  other 
ways  in  which  it  may  have  been  derived  from  a  series  of  parallel  rays, 
and  I  oifer  this  merely  as  the  most  probable  interpretation  so  far  as  I 
can  now  see.  Fig.  71  does  the  same  for  the  hind  limb  of  Crypto- 
branchus  Japonicus.  The  curvature  of  the  rays  has  been  exhibited 
in  a  marked  degree  quite  frequently  in  Elasmobranch  median  fins. 

The  Innervation  of  the  Paired  Fins. 
I  have  made  complete  and  definite  observations  of  the  innervation 
only  in  a  single  case,  namely  in  the  pectoral  fin  of  Mustelus  canis. 
This  fin  is  supplied  by  the  first  15  niyeh»nal  nerves  together  with  a 
very  small  branch  from  the  vagus.  The  simplest  condition  is  seen  in 
the  aborad  nerves. 


*  Phil.  Trans.,  vol.  clxi,  Pt.  ii,  p.  534.         f  Uiiters.,  Hft.  iii,  p.  181,  note. 
X  MuUer's  Archiv,  1845,  p.  8. 


J.  K.  Thacher — Median  and  Paired  Fins.  305 

The  aborad  four  (12-15)  branches,  coming  directly  from  the 
myelon,  advance,  each  by  itself,  close  to  the  metai)teryoiuni,  where 
they  each  bifurcate,  sending  one  branch  to  the  dorsal  and  the  other 
to  the  ventral  side  of  the  tin.  The  next  four  (S-11)  unite  to  form  a 
rather  loose  plexus,  which  separates  again  into  four  nerves,  wiiich 
then  sub-divide  in  the  same  way  as  the  last  mentioned  four,  except 
that  the  orad  of  these  behaves  a  trifle  differently  in  a  manner  here- 
after to  be  described. 

Now  the  first  seven  nerves  unite  with  one  another  and  with  the 
minute  branch  of  the  vagus  in  the  following  way.  The  vagal  branch 
emerges  from  the  skull  with  that  nerve,  but  already  rolled  up  as  a 
separate  branch  and  easily  to  be  separated  from  it;  this  joins  the 
first  myelonal  nerve  and  this  the  second,  and  their  sum  the  third,  and 
so  on,  until  we  have  a  cord  formed  of  the  vagal  and  first  seven 
myelonal  branches.  This  sends  ofi'  a  branch  to  the  muscles  and 
integument  in  front  of  the  shoulder  girdle,  but  the  main  part  of  it 
proceeds  on  its  way  to  enter  the  foramen  called  by  Gegenbaur, 
liiintriUsoffming^  and  then  divides  within  the  cartilage  of  the  girdle 
in  the  way  which  he  has  described,  and  similarly  to  the  aborad  nerves 
which  he  has  left  unnoticed,  sending  one  branch  to  the  dorsal  and  the 
other  to  the  ventral  muscles  of  the  fin.  Now  the  eighth  nerve  sends 
off  its  ventral  branch  like  those  aborad  of  it,  but  the  dorsal  branch 
enters  the  entrance-opening  with  the  cord  of  the  vagus  and  1-7  spinal 
nerves;  but  it  does  not  unite  with  this  cord  till  after  the  latter  has 
divided,  and  then  unites  with  its  dorsal  branch  and  emerges  with  that 
from  the  cartilage  on  the  dorsal  side  of  the  fin.  In  another  specimen, 
this  dorsal  branch  of  the  eighth  nerve  enters  the  cartilage  by  a  minute 
separate  foramen,  but  unites  with  the  dorsal  branch  of  the  anterior 
cord,  as  in  this  case. 

As  stated,  my  observations  in  the  other  cases  have  not  been  as 
thorough,  and  I  cannot  give  the  number  of  ner\es,  but  in  the  ventral 
fin  the  arrangement  is  as  follows.  A  number  of  nerves  are  gathered 
together  to  form  the  orad  cord.  This,  on  coming  opposite  the  fora- 
men in  the  pelvic  girdle,  divides  and  sends  its  branch  to  the  ventr^il 
side  of  the  fin  through  that.  Then  the  other  aborad  nerves  coming 
out,  each  by  itself,  to  the  metapterygium  divide  into  two  branches  for 
the  two  sides  of  the  fin,  just  as  in  the  case  of  the  pectoral  fin.  This 
is  in  3Iustehis  canis. 

In  Eugomphodus  Htor(dls,  see  PI.  LX,  fig.  00,  from  the  articulation 
of  two  or  three  rays  with  the  girdle,  aborad  of  those  which  by  their 
concrescence  mark  themselves  out  as  the  pro])terygiuni,  it  appears 

Trans.  Conn.  Acad.,  Vol.  HI.  39  February,  1877. 


306  J.  K.  Thacher — Median  avd  Paired  Fins. 

that  the  articulation  (or  failure  of  concrescence)  of  the  metapterygium 
and  girdle  has  taken  place  farther  aborad,  and  consequently  a  greater 
number  of  rays  devote  their  basal  parts  to  the  formation  of  the  pelvic 
girdle.  Expectedly  then,  we  find  that  the  cartilage  does  in  fact 
spread  around  the  branches  of  the  next  two  nerves.  Through  the 
foramina  the  ventral  branches  of  these  nerves  pass,  while  the  branches 
to  the  dorsal  side  pass  along  to  that  side  above  the  cartilage. 

The  difference  in  respect  to  the  relation  between  the  cartilage  and 
the  nerves  in  the  pectoral  and  ventral  limb  is,  that  in  the  former  the 
cartilage  thickens  so  as  to  include  the  branching  place  of  the  first 
nerve  or  bundle  of  nerves,  while  in  the  pelvic  limb,  it  is  thinner  and 
merely  transmits  the  ventral  branch.  In  his  Memoir  on  the  Shoulder 
Girdle,  Gegenbaur  has  called  attention  to  the  two  branching  canals 
or  two  pairs  of  openings  in  the  shoulder  girdle  of  the  Batoidei.  He 
states  that  he  has  not  observed  whether  the  aborad  one  is  traversed 
by  a  nerve.  I  have  examined  this  in  the  case  of  Raia  erinaceus,  and 
found  that  both  fore  and  after  openings  transmit  nerves  in  the  same 
way.  This  is  evidently  what  would  be  anticipated  from  what  has 
been  herein  said.  We  have  here  what  we  had  in  the  ventral  fin 
(and  girdle)  of  Eugoniphodxis  ;  a  greater  number  of  rays  are  devoted 
to  girdle  building,  and  another  bundle  of  nerves  is  included  in  the 
spreading  cartilage. 

The  observations  of  Rolph  on  the  innervation  of  Amphioxus^  are  in 
complete  agreement  with  what  would  be  required  by  the  view  here 
advocated.  He  says  "  Der  ventrale  Ast  verlauft  herab  bis  in  die 
Seitenfalten.  Beim  Eintritt  in  dieselben  theilt  er  sich  in  zwei  Aeste, 
deren  einer  {}%^  an  der  Aussenwand  der  Seitenfalte  hinzieht;  der 
andere  durchlaiift  die  Seitenfalte  in  querer  Richtung,  um  in  die 
Bauchmuskulatur  tiber  zu  treten,  in  der  er  sich  nicht  weiter  verfolgen 
lassen.  Zuvor  jedoch  gibt  er  noch  einen  Zweig  ab  (^ig),  welcher,  n^ 
parallel,  an  der  inneren  Wand  der  Seitenfalte  verlauft." 

The  manner  of  innervation,  then,  seems  to  me  as  totally  inconsistent 
with  the  Archipterygium  theory  as  it  is  in  thorough  and  telling  har- 
mony with  the  view  which  I  have  here  presented. 

Addendum. 

Since  the  views  expressed  in  the  foregoing  pages  were  complete  in 
my  own  mind  six  or  eight  months  ago,  I  had  looked  for  confirmation 
of  them  in  the  brilliant  investigations  of  Balfour  on  the  development 

*Morph.  Jahrb.,  Bd.  ii,  Hft.  1,  p.  107,  1876. 


J.  K.  Tluicher — Median  and  Paired  Fins.  ;507 

of  Elasmobranchs.  Tlie  preliininary  account,  however,  in  the  Journal 
of  Microscopical  Science,  contained  nothiuij;  bearing  on  the  point,  and 
the  pa])ers  in  tlie  Journal  of  Anatomy  and  Physiology  I  have  been 
able  to  obtain  only  irregularly.  Immediately  after  the  hist  proof  of 
the  preceding  pages  had  been  received,  tlie  number  of  that  Journal 
for  October,  1876,  came  into  my  hands.  Here  Balfour  devotes  three 
or  four  pages  to  the  limbs.  He  says :  "  If  the  account  just  given  of  the 
development  of  the  limb  is  an  accurate  record  of  what  really  takes 
place,  it  is  not  possible  to  deny  that  some  light  is  thrown  by  it  upon 
the  first  origin  of  the  vertebrate  limbs.  The  fact  can  only  bear  one 
interpretation,  viz:  that  the  limbs  are  the  remnants  of  continuous 
lateral  fins.'''' 

"The  development  of  the  limbs  is  almost  identically  similar  to  that 
of  the  dorsal  fins."  He  goes  on  to  state  that  while  none  of  his 
researches  throw  any  light  on  the  nature  of  the  skeletal  parts  of  the 
limb,  they  certainly  lend  no  support  to  Gegenbaur's  view  of  their 
derivation  from  the  branchial  skeleton.  Thus  these  results  have  not 
only  been  reached  independently,  but  from  two  different  classes  of 
facts.  To  the  belief  in  the  original  continuity  of  the  lateral  fins  and 
the  homodynamism  of  median  and  paired  fins  I  was  led  by  observa- 
tions on  adult  forms,  and  particularly  on  the  skeleton.  Balfour  comes 
to  the  same  results  from  embryological  investigations,  in  that  group 
from  which  on  general  grounds  an  answer  was  most  to  be  expected ; 
nor  do  these  investigations  regard  the  skeleton. 

I  have  also  just  received  the  last  number  of  the  Morph.  Jahrb.  It 
contains  a  paper  by  Wiedersheim*  confirming  Gegenbaur's  view 
respecting  the  double  nature  of  the  centrale.  This  had  previously 
been  shown  only  in  the  tarsus  of  Cryptobranchus  Japonicus,  (and  in 
the  Enaliosaurs).  Wiedersheim  shows  its  double  character  in  three 
Siberian  species  of  Urodela,  in  both  carpus  and  tarsus.  This  is  a  very 
important  confirmation  of  the  chiropterygium,  and  relieves  us  of  sus- 
picions with  regard  to  its  correctness  Avhen  we  push  our  inquiries 
into  earlier  history  and  more  simple  forms. 

In  the  same  number  of  the  Jahrbuch  is  a  paper  by  Gegenbaurf  on 
the  archipterygium  theory.  He  modifies  his  explanation  of  the 
Stapediferal  limb  to  accord  with  Huxley's  view  of  the  homology  of 
edges  and  faces  of  limb  and  fin.     He  says  that  while  he  does  not 


*  Morph.  Jahrb.,  Bd.  ii,  Hft.  3.     R.  "Wiedersheim,  Die  altesten  Formen  des  Carpus 
und  Tarsus  der  heutigen  Amphibien. 

f  C.  Gegenbaur,  Zur  Morphologie  der  GHedmaassen  der  Wirbelthiere. 


308  J.  K.  Thachet — Median  and  Paired  Fins. 

think  the  correctness  of  this  view  fully  demonstrated,  still  he  thinks 
there  is  a  decided  balance  of  probability  in  its  favor.  Therefore  the 
ulnar  side  of  the  arm  now  appears  as  the  Stammreihe.  In  other 
particulars  Gegenbaur  reaffirms  his  previous  views.  He  proceeds  to 
devote  considerable  space  to  the  discussion  of  the  origin  of  the 
archipterygium,  and  again  proposes  to  assimilate  the  limb  and  limb- 
girdles  to  the  gill-arches  with  their  rays.  He  supports  this  sugges- 
tion with  considerable  argumentation.  To  this  position  the  archip- 
terygium theory  leads  him. 


I  take  this  opportunity  for  expressing  my  sense  of  the  great  advan- 
tages furnished  by  the  U.  S.  Fish  Commission  for  the  study  of  marine 
life  on  our  coasts,  and  in  particiilar  by  the  biological  laboratory  at 
Wood's  Hole,  established  in  connection  with  that  Commission,  and 
also  for  acknowledging  my  personal  indebtedness  to  Professor  Baird, 
through  whose  courtesy  I  have  enjoyed  these  facilities  for  a  number 
of  summers. 


J.  K.  Tliacher — Median  and  Paired  Fins.  309 


EXPLANATION  OF  PLATES. 

The  figures  are  all  drawn  with  a  camera,  and  photo-lithographed.  They  are  all 
three-fourths  of  the  size  of  the  originals,  except  figs.  1,  2,  3,  4,  20,  21,  22,  60;  figs. 
20,  21  and  22  are  three -eighths,  and  60  is  a  little  less  than  twice  natural  size. 

Plate  XLIX. 

Figure  l.  —  Petromyzoa  mariiitis.     a,  Ligamentum  longitudinale,  or  ridge-pole  of  my- 

elonal  canal ;  b,  notochord ;  c,  neural  arches. 
Figure  2. — Petromyzon  marinus.     a,  fin -rays  ;   &,  intermuscular  septa. 
Figure  3. — Petromyzon  marinus.     a,  fin-ray;  b,  fin-muscles. 
Figure  4. — Section  of  Petromyzon  marinus,  to  show  the  relation  of  the  neural  arches  to 

the  muscular  segments  ;  a,  intermuscular  septum  ;  &,  neural  arch ;  c,  blood-vessel ; 

d,  muscular  segment ;  e,  fatty-fibrous  ridge-pole  of  neural  canal. 
Figures  5,  6. — Mustelus  canis.     First  dorsal. 

Plate  L. 

Figures  7-10. — Mustelus  canis.     First  dorsal. 
Figure  11. — Mustelus  canis.     Second  dorsal. 

Plate  LI. 

Figures  12-15. — Mustelus  canis.     Second  dorsal. 
Figures  16,  17. — Mitstelus  canis.     Anal. 

Plate  LII. 

Figures  18,  19. — Mustelus  canis.     Anal. 
Figure  20. —  Galeocerdo  tigrinus.     First  dorsal. 
Figure  21. —  Galeocerdo  tigrinus.     Second  dorsal. 
Figure  22. —  Galeocerdo  tigrinus.     Anal. 
Figure  23. — Eidamia  Milberti.     First  dorsal. 

Plate  LIII. 

Figure  24.  —  Eidamia  Milberti.     First  dorsal. 
Figures  25.  26. —   ''  "  Second  dorsal. 

Figures  27,  28.—   "  "  Anal. 

Figure  29. — S-phyraa  zijgcena.     First  dorsal. 

Plate  LIV. 

Figure  30. — Sphyrna  zygcena.     First  dorsal. 

Figure  31. —       ''  "  Second  dorsal. 

Figure  32.—        '  ''  Anal. 

Figures  33-35. — Eugomphodus  { Odontaspis)  litoralis.     First  dorsal. 

Plate  LV. 
Figures  36-39. — Eugomphodus  litoralis.     First  dorsal. 
Figures  40,  41. —  "  "  Second  dorsal. 

Plate  LVT. 
Figures  42-46. — Eugomphodus  litoralis.     Second  dorsal. 
Figures  47,  48.—  "  "  Anal. 


310  J  K.  Thacher — Median  and  Paired  Fins. 

Plate  LVII. 
Figures  49,  50  — Eugomphodus  litoralis.     Anal. 
Figures  51-54. — Squalus  (Acanthias)  Americcmus.     First  dorsal. 

Figures  55,  56. —       "  "  "  Second  dorsal.      The  spine  is  re- 

moved in  figs.  53,  55,  57  ;  but  not  in  ligs.  51,  52,  54,  56. 

Plate  LVIII. 

Figure  57. — Squalus  Americanus.     Second  dorsal. 

Figure  58. — Baia  levis.     First  dorsal. 

Figure  59. —    "       "         Second  dorsal. 

Figure  60. — Myliohatis  Fremenvillei.     Sole  dorsal. 

Figure  61. — Acipenser  brevirostris.  Sole  dorsal;  a,  neural  arch;  6,  intercalary  carti- 
lages ;  c,  neural  spine ;  d,  foramen  for  ventral  branch  of  spinal  nerve ;  e,  foramen 
for  dorsal  branch  of  spinal  nerve. 

Plate  LIX. 

Figure  62. — Acipenser  brevirostris.    Anal.     Opposite  2-|  vertebrae. 

Figure  63. — Section  of  vertebrarium  of  Acipenser  brevirostris;    a,   neural   spine;  6, 

ligamentum  longitudinale ;  c,  neural  arch. 
Figure  64. — Acipenser  brevirostris,  left  ventral,  from  above  ;  a,  iliac  process. 
Figure  65. — Acipenser  brevirostris,  portion  of  right  ventral,  from  below. 
Figure  66. — Section  of  pectoral  fin  of  Mustelus  canis. 
Figure  67. — Mustelus  canis,  ventral. 
Figure  68. — Mustelus  canis,  pectoral  detached  from  girdle. 

Plate  LX. 

Figure  69. — Eugomphodus  litoralis.     Ventrals;  a,  b  and  c  nerve-foramens. 

Figure    70. — Pectoral  limb  of  Ichthyosaurus,  after   Cuvier.       Car.,   carpalia ;    Cen., 

centralia ;  u,  ulnare ;  i,  intermediiun  ;  r,  radiale ;  U,  ulna ;  R,  radius ;  II,  humerus. 

I  take,  though  with  some  hesitation,  Gegenbaur's  indentification  of  the  radial  and 
ulnar  sides  in  this  limb  of  IcMhyosaurv,s. 
Figure  71. — Gryptobranchus  Japonicu^s.  Hind  foot,  after  Hyrtl,  Schediasma  anatomicum, 

1865. 


VIII. — The  Early  Stages  of  Hippa  talpoida,  with  a  note  on 
THE  Structure  of  the  Mandibles  and  Maxillj?  in  Hippa  and 
Remipes.     By  Sidney  I.  Smith. 

The  biological  station,  established  under  the  auspices  of  the  United 
States  Commissioner  of  P^ish  and  Fisheries,  at  Wood's  Hole,  Massa- 
chusetts, during  the  summer  of  1875,  afforded  several  naturalists,  and 
among  them  the  writer,  excellent  facilities  for  studying  the  marine 
animals  of  Vineyard  Sound  and  the  adjacent  waters.  The  locality  is 
very  favorable  for  obtaining  in  abundance  the  free-swimming  larvjB 
of  a  great  variety  of  marine  animals.  Among  the  young  of  numerous 
species  of  crustacea,  the  zoeae  o^  Hippa  were  particularly  interesting, 
and  I  svicceeded  in  obtaining  a  nearly  complete  series  of  the  post- 
embryonal stages  of  that  peculiar  genus. 

Since  almost  nothing  has  been  published  in  regard  to  the  habits  of 
any  of  the  species  of  Hippidaj  or  Albunidae,  a  few  words  in  regard  to 
the  habits  of  the  only  species,  of  either  Fig.  i.- 

of  these  groups,  living  upon  the  coast 
of  New  Elngland  may"  not  be  out  of 
place  here. 

Hippa  talpoida  inhabits  the  entire 
eastern  coast  of  the  United  States  from 
Cape  Cod  southward  to  the  west  coast 
of  Florida ;  Egmont  Key  being  its  most 
southern  and  western  habitat  known 
to  me.  At  what  point  it  is  met  or 
replaced  by  the  Brazilian  H  emerita, 
I  am  unable  to  determine,  never  having 
seen  specimens  of  either  species  from, 
or  the  record  of  their  occurrence  in, 
the  West  Indies  or  Central  America, 
although  some  species  of  the  genus 
probably  inhabits  both  these  regions. 
On  the  sandy  coasts  of  the  southern  United  States  the  H.  talpoida  is 
apparently  very  abundant,  while  on  the  coast  of  New  England  it  is 
much  less  common,  being  found  only  in  special  localities,  although, 

*  Hippa  talpoida,  adult  female  with  the  antennae  extruded,   dorsal  view,  enlarged 
about  two  diameters. 
Trans.  Conn.  Acad.,  Vol.  III.  40  April,  1877. 


3 1 2  S.  I.  ^%nU7i — Early  Star/es  of  Hippa  talpoida. 

from  its  gregarious  habits,  it  is  usually  found  in  al)undauce  in  such 
localities.  The  northern  range  of  this,  as  well  as  of  numerous  other, 
southern  species  is  undoubtedly  resti'icted  by  the  extreme  cold  of  the 
winters  ;  and  exceptionally  cold  seasons  probably  destroy  a  large 
part  of  the  individuals  over  considerable  portions  of  the  coast. 
Dui'ing  the  summer  of  1870  not  a  specimen  of  the  adult  or  half 
grown  Hippa  could  be  found  at  Fire  Island  Beach,  Long  Island, 
although  the  extensive  sandy  beaches  of  that  region  offer  specially 
favorable  localities,  which  were  thoroughly  searched ;  but  during  the 
last  of  August  and  early  September,  the  young  just  changed  from  the 
zoea,  and  also  in  a  little  later  stage,  appeared  abundantly  upon  the 
beaches.  During  the  following  summer  no  fully  grown  specimens 
were  found  on  the  shores  of  Vineyard  Sound,  though  half  grown 
specimens  (perhaps  from  the  young  of  the  previous  season)  were 
common.  During  the  summer  of  1875,  fully  grown  specimens  of 
both  sexes  were  found  in  great  abundance  at  a  single,  very  restricted 
locality  near  Nobska  Point,  on  the  shore  of  Vineyard  Sound, 
although  at  this  time  none  could  be  foimd  at  the  particular  locality 
where  they  were  common  in  1871. 

Upon  our  shores,  as  far  as  I  have  observed,  the  Hippa  inhabits 
sandy  beaches  which  are  somewhat  exposed  to  the  action  of  the 
waves.  It  seems  to  prefer  only  a  narrow  zone  of  the  shore,  at  or  very 
near  low  water  mark,  where  it  lives  gregariously,  burrowing  in  the 
loose  and  changing  sands.  At  the  locality  near  Nobska  Point  above 
referred  to,  it  was  obtained  in  great  abundance  by  digging  over  the 
sand  just  at  the  edge  of  the  receding  waves.  Several  individuals 
were  often  thrown  out  at  a  single  stroke  of  the  spade,  but  the  won- 
derful rapidity  with  which  these  animals  burrow  made  it  extremely 
difficult  to  secure  more  than  one  or  two  of  them  at  a  time.  The 
smooth,  oval  form  of  the  animal,  with  the  peculiar  structure  of  the 
short  and  stout  second,  third,  and  fourth  pairs  of  thoracic  legs,  enables 
them  to  burrow  with  far  greater  rapidity  than  any  other  crustacean 
1  have  observed.  Like  many  other  sand-dwelling  crustaceans,  they 
burrow  only  backwards  ;  and  the  wedge-shaped  posterior  extremity  of 
tlie  animal,  formed  by  the  abrupt  bend  in  the  abdomen,  adapts  them 
admirably  for  movement  in  this  direction.  When  thrown  upon  the 
wet  beach,  they  push  themselves  backward  with  the  burrowing  thoracic 
legs  and,  by  digging  with  the  appendages  of  the  sixth  segment  of  the 
abdomen  slightly  into  the  sui-face,  direct  the  posterior  extremity  of 
the  body  downward  into  the  sand.  Upon  the  beaches,  at  least  where 
there   are   any   waves,  they  seem  usually  to   be   buried   completely 


S.  1.  S)i}!f/i—H<(rh/  Stdf/ex  of  Ilippa  talpokht.  :UM 

beneath  tlio  surluce.  Occasionally,  however,  they  are  found  swinnnin^- 
about  in  ])ools  left  by  the  tide,  and  they  undoubtedly,  when  undis- 
turbed, sometimes  come  out  and  swim  in  the  same  way  along  the 
shore,  though  they  probably  never  venture  far  from  tlie  bottom. 

When  first  placed  in  an  aquarium  with  a  few  inches  of  sand  at  the 
bottom,  they  invariably  ])lunged  at  once  entirely  beneath  the  sand, 
but,  after  a  few  moments  of  quiet,  usually  worked  themselves  gradually 
towards  the  surface,  resting  in  a  nearly  perpendicular  position  with 
just  the  tips  of  the  aiitennuhe  and  eyes  at  the  surface,  while  the  ex- 
cui'rent  water  from  the  branchiae  formed  a  small  opening  and  a 
slightly  boiling  motion  in  the  sand.  Occasionally,  when  entirely 
undisturbed,  they  would  suddenly  leave  the  sand  and  swdni  rapidly 
round  the  top  of  the  aquarium  for  a  moment  and  then  dive  suddenly 
to  the  bottom  and  bury  themselves  in  the  sand.  In  swimming,  as 
well  as  in  burrowing,  the  telson  was  carried  appressed  to  the  sternum 
and  they  invariably  moved  backward,  the  motion  being  ap|)arently 
produced  by  the  appendages  of  the  sixth  abdominal  segment  and  the 
anterior  thoracic  legs,  while  the  latter  served  also  as  steering  organs. 

During  all  the  ordinary  motions  of  swimming  and  burrowing,  I 
have  never  seen  the  antenna^  extruded,  although  the  peculiar  arrange- 
ment of  the  peduncular  segments  and  their  complex  system  of  muscles 
are  apparently  specially  adapted  for  extending  and  withdrawing 
these  beautiful  organs.  When  the  animals  are  thrown  into  alcohol 
however,  the  antennre  are  sometimes  thrown  out  convulsively  and 
then  immediately  retracted.  In  life  the  antennae  are  most  of  the 
time  held  in  the  position  in  which  they  are  usually  found  in  alcoholic 
specimens,  that  is,  between  the  second  and  external  maxillipeds,  with 
the  peduncles  crossed  in  front,  and  the  flagella  curved  down  and 
entirely  round  the  mouth  so  that  their  dense  armament  of  sette  all 
project  inward.  When  extruded,  the  distal  segments  of  the  peduncle 
are  revolved  half  way  round  on  the  proximal  ones,  so  as  to  carry  the 
whole  appendage  to  its  own  side  of  the  animal  and  throw  the  curve 
of  the  flagellum  into  a  reversed  position.  Judging  from  the  pecul- 
iarly armed  setae,  of  the  flagella,  one  of  the  principal  offices  of  the 
antenna?  is  the  removal  of  parasitic  growths  and  all  other  foreign 
substances  from  the  appendages  of  the  anterior  portion  of  the  animal. 

The  mouth  parts  of  the  adult  are  not  adapted  for  ordinary  prehen- 
sion or  mastication,  but  I  am  unable  to  make  any  positive  statement 
in  regard  to  the  food  of  these  animals.  In  all  specimens  examined 
the  alimentary  canal  was  filled  with  tine  sand  which  seemed  to  be 
nearly  free  irom  animal  or  vegetable  matter.     The  material  from  the 


314  ^S',  /.  tSnuth — EarJy  St<i<j(>.s  of  Illppa  Udpoidn. 

stomaeli,  however,  shew,  under  the  microscope,  u  small  quantity  of 
vegetable  matter,  and  it  seems  probable  that  the  sand  is  swallowed 
for  the  nutritive  matter  it  may  contain. 

Upon  the  beaches  of  Vineyard  Sound  the  two  sexes  appeared  to 
occur  in  about  equal  numbers,  although  in  museum  collections  the 
males  are  often  rare.  This  is  probably  due  to  the  great  inequality  in 
size  between  the  male  and  female,  the  length  of  the  carapax  in  the 
larger  females  from  Vineyard  Sound  being  20  to  22""",  while  in  the 
largest  males  it  does  not  exceed  14"'"'.  The  sexes  differ  also  in  the 
form  of  the  telson  (Plate  XLVIII,  figs.  7,  8)  which  is  narrower  and 
more  triangular  in  the  male  than  in  the  female. 

Females  carrying  eggs  were  found  during  the  entire  month  of 
August,  and  during  that  period  the  embryos  within  the  eggs  were 
nearly  fully  developed  in  many  of  them.  Undoubtedly,  however,  the 
term  of  carrying  eggs  extends  over  a  much  longer  period  than  this. 
The  eggs  are  nearly  spherical,  "40  to  -45"'"'  in  diameter,  and  the  yolk 
mass  is  orange  yellow  while  the  formed  tissues  of  the  embryo  are 
nearly  colorless.  Numerous  attempts  to  obtain  newly  hatched  young, 
by  keeping  egg-carrying  females  in  aquaria,  failed  from  the  parent 
invariably  casting  off  the  eggs  before  they  were  fully  matured. 
Consequently  I  failed  to  secure  the  earliest  stage  of  the  zoea,  for  the 
youngest  individuals  taken  in  the  towing  net  were  apparently  in  the 
second  stage. 

Very  nearly  fully  developed  embryos,  when  removed  from  the  egg, 
were  found  to  possess  all  the  normal  articulated  appendages  of  the 
fully  formed  zoeae,  but  there  was  no  appearance  of  lateral  spines  upon 
the  carapax  and  the  rostrum  was  broad  and  obtuse.  In  this  stage 
the  embryo  agrees  almost  perfectly  with  the  figure  of  the  zoea  of 
Ilippa  emerita  from  the  coast  of  Brazil,  given  by  Fritz  Mliller  in  his 
work  entitled  "  Ftir  Darwin."*  The  difference  between  the  embryo 
in  this  stage  and  the  second  zoea-stage  (Plate  XLV,  fig.  1),  in  which 

*  English  translation,  London,  1869,  p.  54,  fig.  25.  The  figure  is  accompanied  by 
the  following  paragraph :  "  The  Zoea  of  the  Tatuira  [Hvppa\  also  appears  to  differ  but 
little  from  those  of  the  true  Crabs,  which  it  likewise  resembles  in  its  mode  of  locomo- 
tion. The  carapax  possesses  only  a  short,  broad  frontal  process ;  the  posterior  margin 
of  the  tail  is  edged  with  numerous  short  setse."  This,  as  far  as  I  am  aware,  is  the 
only  published  account  of  the  development  of  any  sjDecies  of  Hippidse,  except  a  note 
by  myself  (in  an  article  on  "  The  Metamorphoses  of  the  Lobster  and  other  Crustacea," 
in  the  Report  of  the  LT.  S.  Commissioner  of  Fish  and  Fisheries,  Part  J,  187."5,  p.  530) 
recording  the  occurrence,  at  the  surface  in  Vineyard  Sound,  of  the  young  in  what  is 
described  further  on  in  these  pages  as  the  megalops-stage. 


S.  r.  SntlfJi  —  KitrJj/  Stat/es  <}f  Tfijypa  t<dpoi(la.  315 

tlio  rostrum  and  lateral  spines  are  enormously  developed,  suggests 
the  possibility  that  MtlUer  had  observed  only  imperfectly  developed 
young  zoea^  in  which  the  rostrum  and  lateral  spines  were  not  ex- 
pamled.  It  seems  scai'cely  probable  that  such  a  difterence  could 
exist  between  the  first  stage  of  the  zoea,  when  the  veiling  membrane, 
in  which,  on  first  escaping  from  the  egg,  the  young  are  usually 
enveloped,  has  been  entirely  cast  oft'  and  the  lateral  spines  and  the 
rostrum  are  fully  expanded,  and  tlie  second  zoea-stage  about  to  be 
described.  The  three  later,  true  zoea-stages  obtained  are  evidently 
contiguous  steps  in  the  development  and  are  here  designated  the 
second,  third,  and  last  stages  of  the  zoea.  From  this  last  stage  the 
zoea  passes  at  once  into  a  stage  closely  resembling  the  adult  in  gen- 
eral form,  but  with  the  eyes  still  very  large  and  the  abdomen  furnished, 
with  powerful  swimming  legs.  This  condition  of  the  animal  corres- 
j)onds  perfectly  to  the  Brachyuran  megalops  and  may  properly  be 
designated  as  the  megalops-stage. 

Second  zoea-stage. 
In  this  stage  the  young  (Plate  XLV,  fig.  1,  ventral  view)  are  a 
little  over  8"""  in  length,  from  tip  of  rostrum  to  the  posterior  margin 
of  the  carapax,  and  a  little  over  2"'"'  between  the  tips  of  the  lateral 
spines.  In  general  form  the  carapax  is  oval,  with  the  smaller  end  for- 
ward, and  its  surface  is  very  smooth  and  regularly  rounded.  The  dorsal 
surface  of  the  carapax  is  strongly  convex  but  very  regularly  rounded 
and  wholly  devoid  of  any  rudiment  of  a  dorsal  spine,  which  is  so 
generally  characteristic  of  the  zoeae  of  Brachyura.  At  the  bases  of 
the  ocular  peduncles  the  carapax  is  shai-ply  contracted  laterally  into 
an  exceedingly  long^  very  slender,  and  slightly  tapering  rostrum 
curved  regularly  downward  until,  toward  the  tip,  it  becomes  nearly 
parallel  M'ith  the  posterior  margin  of  the  carapax.  The  lateral  spines 
are  nearly  as  long  as  the  diameter  of  the  carapax,  are  situated  far 
back  and  low  down  on  the  sides  of  the  carapax,  and  are  directed 
downward  and  obliquely  outward,  but  are  not  strongly  curved. 
Beneath,  the  carapax  ciirves  inward  on  all  sides,  leaving  a  compara- 
tively small  opening  which  is  wholly  inferior,  with  its  anterior  j)ortion 
about  as  broad  as  the  telson,  but  posteriorly  contracted  into  a  narrow 
abdominal  sinus,  of  which  the  rounded  posterior  margin  is  nearly  on 
a  line  between  the  lateral  spines.  This  shortening  of  the  inferior 
opening,  carrying  the  abdomen  forward  and  wholly  beneath  the 
carapax,  together  with  the  absence  of  the  dorsal  spine,  gives  the 
animal  an  apj^earance  unlike  ordinary  Brachyuran  zoese. 


310  iS.  I.  /Smith — Early  Stages  of  Hippo  talpoida. 

The  ocular  peduncles  are  stout,  regularly  tapering  to  near  the 
bases,  and  are  usually  carried  perpendicular  to  the  mesial  plain,  though 
they  admit  of  considerable  motion  in  all  directions.  The  cornea  is 
considerably  larger  than  the  diameter  of  the  peduncle,  its  diameter 
being  nearly  a  third  of  the  horizontal  diameter  of  the  carapax,  and, 
when  the  peduncle  is  held  straight  out,  reaches  slightly  beyond  the 
lateral  margin  of  the  carapax. 

The  antennulae  (Plate  XL VI,  tig.  1)  are  still  rudimentary,  simple, 
sackdike,  unarticulated  appendages,  tapering  towai-d  the  tip,  which  is 
furnished,  as  usual  in  this  stage  of  development,  with  three  stout, 
filiform,  obtuse  setne,  diftering  slightly  in  length,  diameter,  and  amount 
of  curvature,  and  of  which  the  longest  is  about  half  the  length  of 
tlie  antennula  itself. 

The  antennse  (Plate  XLVI,  tig.  2)  are  of  about  the  same  length  as 
the  antennula-,  but  of  nearly  the  same  diameter  throughout,  and  are 
armed  distally,  at  the  outer  edge,  with  an  acute,  dentiform  process 
(a,  fig.  2)  directed  straight  forward  and  itself  armed  with  a  minute, 
setiform  spine  on  the  inner  edge  near  the  tip.  Between  the  base  of 
this  process  and  a  slight,  rounded  prominence  (c,  fig.  2),  situated  at 
the  extremity  of  the  inner  margin,  and  which  represents  the  rudiment- 
ary flagellum,  there  is  a  similar,  but  slightly  more  slender,  process 
(b)  attached  at  its  base  by  an  oblique  articulation  and  armed,  near 
the  tip,  with  a  minute,  setiform  spine  like  that  upon  the  outer  process. 

The  oral  appendages  differ  very  little  from  their  condition  in  the 
last  zoea-stage,  under  which  they  are  fully  described.  The  labrum 
and  labium  differ  scarcely  at  all,  except  in  size,  in  the  three  zoea- 
stages  here  described.  The  labrum,  as  seen  from  beneath,  is  a  broad, 
somewhat  triangular  prominence  between  the  bases  of  the  antennulae 
and  the  tips  of  the  mandibles.  The  labium  is  deeply  bilobed,  though 
far  less  deeply  than  in  the  adult,  with  the  lobes  broadly  rounded  and 
the  entire  margin  clothed  with  microscopic  hairs. 

The  mandibles  are  nearly  as  in  the  last  zoea-stage.  They  are  stout 
at  the  bases,  but  taper  to  very  slender  tips,  which  are  only  slightly 
different  on  the  right  and  left  side.  There  is  no  molar  area,  but  the 
crown  of  the  mandible  is  longest  in  a  vertical  direction  and  is  armed 
inferiorly  with  four  long,  but  blunt,  teeth  which  decrease  rapidly  in 
size  as  they  approach  the  middle  of  the  crown,  where  they  are  met 
by  a  series  of  six  or  seven  long,  slender,  setadike  processes  which 
occupy  the  superior  half  of  the  coronal  margin. 

The  first  pair  of  maxilhie  (Plate  XLVI,  fig.  11)  are  symmetrical 
and  composed  of  the  same  parts  as  in  the   adult.     The  inner  lobe 


S.  T.  Snrit})  —  J^arly  Sfafies  of  Hippo,  talpotda.  '.\\1 

{a,  fig.  1 1)  is  small  and  ti|)])t'(l  with  tliroc  long  seta\  Tlie  outer  lobe 
[h,  fig.  11)  is  broader  than  tlie  inner  and  armed  at  the  extremity 
with  three  nearly  equal,  long  and  slender  teeth,  of  which  the  distal 
one  appears  like  a  process  from  the  margin,  showing  no  line  of  artic- 
ulation at  its  base.  The  palpus  ('*,  fig.  11)  is  very  small,  composed 
of  a  single  segment  and  tipped  with  a  long,  plumose  seta. 

The  second  pair  of  maxilla?  (Plate  XLYII,  fig.  l)  are  very  imperfect. 
The  protognath  (</,  fig.  1)  is  a  small,  obtuse  lobe  tipped  with  three 
short  setse.  The  scaphognath  (<■%  fig.  1)  projects  beyond  it  anteriorly 
as  a  slightly  larger  lol^e,  while  posteriorly  it  is  broad  but  short  and 
truncated,  and  the  anterior  lobe  and  the  oi;ter  edge  are,  as  yet,  alone 
furnished  with  seta?. 

The  first  and  second  pairs  of  maxillipeds,  or  natatory  legs,  (Plate 
XLV,  fig.  1,  second  pair)  are  similar  in  structure  to  those  of  most 
zoea^  and  differ  only  slightly  from  each  other.  In  both  pairs  the  basal 
portion,  or  protognath,  is  alike  stout,  about  as  long  as  the  exognath, 
and  unarmed,  except  by  three  or  four  minute  setfe  on  the  distal  portion 
of  the  inner  margin.  The  exognaths,  or  natatory  branches,  alike  in 
both  pairs,  are  nearly  cylindrical,  but  flattened  at  the  tips,  where  they 
each  bear  a  series  of  eight  slender,  plumose  setae,  which,  in  the  middle, 
are  as  long  as  the  exognath  itself  but  decrease  in  length  to  the  outer 
ones,  which  are  scarcely  more  than  tw^o-thirds  as  long.  The  inner 
branch,  or  endognath,  in  both  pairs,  is  composed  of  four  cylindrical 
segments  subequal  in  length.  In  the  first  pair,  however,  the  inner 
branch  is  shorter  than  the  exognath,  while  in  the  second  pair  it  is 
considerably  longer.  In  both  pairs  the  three  proximal  segments  of 
the  endognath  are  each  ai-med  with  two  or  three  small  setje  on  the 
inner  side,  and  the  distal  segment,  which  is  much  more  slender  than 
the  others,  is  tipped  with  four  setae,  of  which  two  are  nearly  as  long 
as  the  segment  itself  and  pectenated  with  minute,  setiform  spinules 
along  one  side,  and  the  two  others  shorter  and  apparently  unarmed. 

The  third  pair  of  maxillipeds  and  the  four  antei-ior  pairs  of  thoi-acic 
legs  are,  even  at  this  early  state,  represented  by  a  series  of  clearly 
defined,  though  entirely  nnsegmented,  processes  situated  just  above 
and  back  of  the  bases  of  the  second  maxillipeds  and  entirely  wnthin 
the  carapax,  but  visible  through  it,  in  a  lateral  view  of  the  animal,  in 
a  line  nearly  parallel  with  the  posterior  margin  of  the  carapax.  In 
the  single  specimen  examined,  no  lobes  representing  the  slender, 
posterior  thoracic  legs  of  the  adult  could  be  discovered.  Above  each 
of  the  processes  representing  the  first  four  pairs  of  thoracic  legs  there 
is  a  minute,  papilliform  process  apparently  representing  one  of  the 
branchial  appendages  belonging  to  these  legs  in  the  later  stages. 


318  S.  I.  Smith  —  hJiirlj/  SUiffcH  of  Ilippa  tdlpoiihi. 

The  iilxlouu'i)  is  smaller  aiul  has  much  less  freedom  of  motion  in  the 
mesial  phmc  than  in  most  Brac^hynran  zoea^  The  first  segment  is 
not  clearly  (litt'erentiated  from  the  thorax.  The  second,  third,  fourth, 
and  fiftli  segments  are  entirely  without  ap))endages;  the  second  and 
third  are  nearly  equal  in  length  and  sub-cyrnuli-ical  ;  the  fourth  is 
slightly  shoi'ter  and  is  exj)anded  considerably  at  the  posterior  ex- 
tremity ;  and  the  fifth  is  about  as  long  as  the  fourth,  compressed 
vertically,  and  broadly  exj)anded  at  the  posterolateral  angles  so  that 
it  is  about  twice  as  broad  as  long.  The  sixth  segment  is  consolidated 
with  the  tclsoii,  forming  a  broad,  lamelliform,  caudal  a])pendage  about 
as  long  as  tlu'  middle  breadth  of  the  caraj)ax.  The  a])pcndages  of  the 
sixth  segment  (Plate  XLVIII,  fig.  10)  ai-e  small,  rudimentary, 
Oppressed  to  the  under  side  of  the  telson  so  as  to  be  hidden  from 
above,  and  are  eac^h  (composed  of  a  stout  basal  segment  and  a  single 
narrow  lamella  (the  outer)  tipped  with  two  slender  setse,  of  which  the 
outer  is  about  as  long  as  the  lamella  itself  and  the  inner  much  longer. 

The  lateral  nuirgins  of  the  telson  are  slightly  curved  outward  aiul 
unarmed,  but  project  )»osteriorly  into  a  stout  tooth  each  side  of  the 
strongly  arcuate  ]»osterior  margin.  This  postei  ior  margin  has,  in  all 
tile  zoea-stages  here  described,  a  remarkably  complex  armament  of 
ciliated  spines  and  miuute  teeth  (Plate  XLVIII,  tigs.  1:5,  14,  15).  In 
a  considerable  iiumbei-  of  specimens  in  tlu'  third  and  the  last  stages, 
the  mnnber  of  these  ciliated  sj)ines  is  usually  twenty-six,  of  whicli 
the  eighth,  counting  (Voni  either  side,  is  the  largest,  and  the  sixth 
and  tenth  usually  the  next  in  size.  One  of  the  specinu'us  in  the 
second  stage  (Plate  XLVIII,  iig.  1:5)  conforms  stiiiily  with  this: 
there  arc  two  sub-nu'dian  spines  (r/,  </,  Iig.  i;5)  separated  by  a  single 
denticle,  then  each  side  a  slightly  larger  sj»ine  (A,  h)  separated  from 
the  sub-nu'dian  ones  by  a  single  denticle,  then  four  alternately 
smaller  and  l:irg(>r  spines  [c,  d,  ('.,/')  se|»arated  from  each  other  by 
two  denticles  at  each  intors])ace,  the  outer  (/')  of  these  four  sjtines 
beino"  the  eighth,  c(»unting  from  either  side,  ami  the  largest.  Outside 
this  large  sjtine  there  arc,  each  side,  seven  smaller  sj)iiu's  separated  by 
interspaces  which  increase  toward  the  outer  margin  and  are  armed 
with  from  two  to  nine  denticles.  The  space  between  the  outer  spine 
each  side  and  the  tooth  of  tlu'  lateral  margin  is  gri'ivtei-  than  any  of 
the  interspaces  bctwi-en  the  spines  and  is  armed  with  twelve  or  thir- 
teen denticles.  In  the  other  specimen  in  this  stage  there  are  only 
twenty-five  spines,  a  single  niediiin  spine  (Plate  XIA'III,  tig.  14,^^) 
taking  the  place  of  the  two  sub-nu'dian  spines  and  the  denticle 
between  them  ;  otherwise  the  Sj)ini'S  and  denticles  are  essentially  as  in 


S.  I.  S/tr/'f/i — Earl;/  Stages  of  Hippa  talpolda.  310 

the  first  specimen  and  as  in  tlio  succeeding  stages.  This  is  appar- 
ently an  abnormal  variation  in  the  armament  of  the  telson.  The 
arrangement  of  these  spines,  and  especially  whether  they  be  odd  or 
even  in  number,  I  have  usually  found  a  constant  character  for  distin- 
guishing the  larval  forms  in  different  groups  of  Podophthalmia. 

Of  this  stage  only  two  specimens  Avere  secured,  one  taken  on  the 
evening  of  September  4,  the  other  in  the  day-time  the  next  day.  In 
coloration  and  habits  they  agreed  essentially  with  the  young  in  the 
succeeding  zoea-stages. 

Third  zoea-stage. 

In  general  form  and  a]»]K'arance  the  zoeas  in  this  stage  very 
closely  resemble  those  in  the  second,  although  they  have  increased 
considerably  in  size,  and  especially  in  the  length  of  the  rostrum, 
which  is  relatively  longer  and  more  slender.  They  are  about  4"5""" 
in  length,  from  the  ti])  of  the  rostrum  to  the  posterior  mai'gin  of  the 
cara})ax,  and  nearly  :V""'  between  the  tips  of  the  lateral  spines. 

The  ocular  peduncles  and  eyes  have  increased  only  slightly  in  abso- 
lute size  and  are  relatively  smaller  than  in  the  second  stage. 

The  antennuhe  liave  changed  very  little.  There  is,  as  yet,  appar- 
ently no  distinction  of  peduncle  and  fiagellum,  although  the  two  or 
three  distal  segments  of  the  latter  are  faintly  indicated,  and,  on  the 
inner  side,  there  are  two  or  three  filiform  setae  on  tlie  penultimate 
segment  in  addition  to  the  three  on  the  terminal  segment. 

The  antennae  (Plate  XLVI,  fig.  ;3)  have  increased  in  size  but  show 
no  indication  of  segmentation.  The  two  dentiform  processes  (a,  ft, 
fig.  3)  have  each  two  or  three  minute  spir.ules  at  the  tip,  but  are 
otherwise  unchanged  ;  the  fiagelluin  (c,  fig.  3),  however,  has  increased 
so  as  to  project  beyond  the  tips  of  the  dentiform  processes  and  show 
))laiiily  its  true  character. 

The  labrum,  labium,  mandibles,  and  first  maxillse,  excej)t  in  size, 
do  not  differ  appreciably  from  their  condition  in  the  second  stage. 
The  second  maxillae  differ  but  little,  the  scaphognath  being  a  little 
more  elongated  posteriorly,  so  as  to  approach  slightly  its  form  in  the 
next  stage. 

The  first  and  second  pairs  of  maxillipeds  differ  from  those  of  the 
first  stage  only  in  the  exognaths,  which  are  each  furnished  with  ten 
instead  of  eight  terminal  seta'. 

The  lobes  representing  the  third  pair  of  maxillipeds  and  the  four 
anterior   pairs  of  thoracic    legs  have   increased    much    in    size,   are 

Trans.  Conn.  Acad.,  Vol.  III.  41  April,  1877. 


820  S.  I.  Smith — Early  Stages  of  Hippa  talpoida. 

curled  up  closely  beneath  the  sternum,  and,  in  all  the  specimens 
examined,  show  the  segments  of  the  succeeding  stage  faintly  indi- 
cated within.  The  posterior  thoracic  legs  appear  to  be  represented 
by  a  small  process  each  side,  just  back  of,  and  nearly  hidden  by,  the 
rudimentary  fourth  pair.  Four  pairs  of  gills  on  each  side  are  repre- 
sented by  two  slender  processes,  one  above  the  other,  at  the  bases  of 
each  of  the  four  anterior  pairs  of  legs 

The  proximal  segments  of  the  abdomen  are  almost  exactly  as  in 
the  previous  stage,  except  there  are  very  slight  elevations  beneath 
the  second,  third,  fourth,  and  fifth  segments,  where  the  rudimentary 
legs  are  to  appear  in  the  succeeding  stage.  The  sixth  segment  is 
still  consolidated  Avith  the  telson.  Its  appendages  (Plate  XLVIII, 
fig.  11)  have  increased  much  in  size  and  the  inner  lamella  (c,  fig.  11) 
has  appeared  as  a  small,  sack-like  appendage  at  the  base  of  the  outer 
lamella  {b,  fig.  11),  which  is  twice  as  long  as  in  the  previous  stage, 
very  narrow,  only  slightly  expanded  in  the  middle,  and  sub-truncate 
at  the  extremity,  where  it  is  furnished  with  four  slender  and  curved 
setoe,  of  which  the  median  ones  are  longer  than  the  lamella  itself, 
while  the  outer  are  little  moj-e  than  half  as  long.  The  telson  is  of 
the  same  form  as  in  the  previous  stage  and  has  the  same  number  of 
ciliated  spines  in  the  armament  of  the  posterior  border,  while  the 
number  of  denticles  in  the  interspaces  has  considerably  increased, 
though  they  are  not  as  numerous  as  in  the  succeeding  stage.  In  one 
specimen  there  is  the  same  abnoi-mal  arrangement  of  the  spines 
described  under  the  second  stage,  that  is,  there  are  only  twenty-five 
spines  in  all,  one  median  spine  taking  the  place  of  the  two  sub-median 
spines  and  the  denticles  separating  them. 

The  young  in  this  stage  were  taken  on  several  occasions,  both  in 
the  day-time  and  evening,  from  August  28  to  September  8.  Their 
habits  and  coloration  in  life  were  the  same  as  in  the  last  zoea-stage. 

Last  zoea-stage. 

The  length  from  the  tip  of  the  rostrum  to  the  posterior  margin  of 
the  carapax  and  the  breadth  between  the  tips  of  the  lateral  spines 
are  nearly  twice  as  great  as  in  the  second  stage,  while  the  rostrum  is 
relatively  considerably  longer  than  in  either  the  second  or  the  third 
stage,  its  entire  length  being  nearly  twice  that  of  the  carapax  proper. 
The  general  form  and  appearance  of  the  young  in  this  stage  are 
shown  upon  Plate  XLV,  figs.  2,  3,  4. 

The  eyes  and  ocular  pediincles  are  very  little  larger  absolutely 
than   in  the  last  stage.     The   diameter  of  the  cornea  is  scarcely  a 


S.  I.  Smith — E((rh/  Stagefi  of  Hippa  talpoida.  :i21 

fourth  the  horizontal  diameter  of  the  carapax  and  the  ocuhir  pedun- 
cles are  slightly  shorter,  proportionally,  than  in  the  earlier  stages. 

In  the  antennulffi  (Plate  XL VI,  fig.  5)  the  segmentation  of  the 
tlagellum  is  carried  nearly  or  quite  to  the  peduncle,  which,  however, 
shows  no  division  into  segments  and  no  clear  separation  from  the 
flagellum.  The  ilagellum  itself  is  composed  of  six  or  seven  segments 
which  are  a  little  broader  than  long  and  of  which  the  terminal  one  is 
furnished  with  three  filiform  setae,  the  penultimate  and  antepenulti- 
mate with  two  or  three  each  which  are  situated  upon  the  inner  side 
at  the  distal  articulations,  while  there  are  two  similarly  situated,  hut 
small  and  i-udimentary  setoe,  upon  the  fourth  segment  from  the  tip. 

The  antenna?  (Plate  XLVI,  fig.  4)  have  increased  very  much  in 
size,  and  the  flagellum  is  much  longer  than  the  peduncle.  The 
peduncle  shows  but  one  distinct  articulation,  which  is  near  the  bases 
of  the  dentiform  processes  and  apparently  represents  the  articulation 
between  the  second  and  third  segments  of  the  fully  developed 
appendage.  The  dentiform  processes  («,  &,  fig.  4)  ar-i  much  more 
slender  and  propoitionally  smaller  than  in  the  third  stage,  but  are 
armed  with  the  same  number  of  spines  at  the  tips.  The  flagellum 
(c,  fig.  4)  externally  shows  no  indication  of  segmentation,  but,  in  all 
the  specimens  examined,  the  articulations  of  the  flagellum  of  the 
succeeding  megalops-stage  is  distinctly  visible  beneath  the  integu- 
ment, as  shown  in  the  figure. 

The  labrum  (Plate  XLVI,  fig.  5,  J),  as  seen  from  beneath,  is  a 
conspicuous,  somewhat  ti'iangular  prominence  between  the  bases  of 
the  antennula?  and  the  mandibles,  with  the  margins  and  the  inferior 
surface  regularly  rounded  and  without  emarginations  at  any  point. 
The  labium  (t?,  fig.  5)  is  deeply  bilobed,  the  regularly  rounded  lobes 
projecting  each  side  of  the  oral  opening  nearly  to  the  tips  of  the 
mandibles  and  having  the  edges  clothed  with  microscopic